Class 12th Mathematics Part Ii CBSE Solution
Exercise 7.1- sin 2x Find an anti-derivative (or integral) of the following functions by the…
- cos 3x Find an anti-derivative (or integral) of the following functions by the…
- e2x Find an anti-derivative (or integral) of the following functions by the…
- (ax + b)^2 Find an anti-derivative (or integral) of the following functions by…
- sin 2x - 4 e3x Find an anti-derivative (or integral) of the following functions…
- Find the following integrals. integrate (4e^3x + 1) dx
- integrate x^2 (1- 1/x^2) dx Find the following integrals.
- integrate (ax^2 + bx+c) dx Find the following integrals.
- integrate 2x^2 + e^x dx Find the following integrals.
- integrate (root x - 1/root x)^2 dx Find the following integrals.
- integrate x^3 + 5x^2 - 4/x^2 dx Find the following integrals.
- integrate x^3 + 3x+4/root x dx Find the following integrals.
- integrate x^3 - x^2 + x-1/x-1dx Find the following integrals.
- integrate (1-x) root xdx Find the following integrals.
- integrate root x (3x^2 + 2x+3) dx Find the following integrals.
- integrate (2x-3cosx+e^x) dx Find the following integrals.
- integrate (2x^2 - 3sinx+5 root x) dx Find the following integrals.…
- integrate secx (secx+tanx) dx Find the following integrals.
- integrate sec^2x/cosec^2xdx Find the following integrals.
- integrate 2-3sinx/cos^2xdx Find the following integrals.
- The anti-derivative of (root x + 1/root x) equalsA. 1/3 x^1/3 + 2x^1/2 + c B.…
- If d/dx f (x) = 4x^3 - 3/x^4 such that f(2) = 0. Then f(x) isA. x^4 + 1/x^3 -…
Exercise 7.10- Evaluate the integrals using substitution. integrate _0^1 x/x^2 + 1 dx…
- integrate _0^pi /2 root sinphi cos^5phi d phi Evaluate the integrals using…
- integrate _0^1sin^-1 (2x/1+x^2) dx Evaluate the integrals using substitution.…
- integrate _0^2root x+2 (putx+2 = t^2) Evaluate the integrals using substitution.…
- integrate _0^pi /2 sinx/1+cos^2xdx Evaluate the integrals using substitution.…
- integrate _0^2 dx/x+4-x^2 Evaluate the integrals using substitution.…
- integrate _-1^1 dx/x^2 + 2x+5 Evaluate the integrals using substitution.…
- integrate _1^2 (1/x - 1/2x^2) e^2x dx Evaluate the integrals using substitution.…
- The value of the integral integrate _ 1/3^1 (x-x^3)^1/3/x^4 dx isA. 6 B. 0 C. 3…
- If f (x) = integrate _0^xtsintegrate dt then f'(x) isA. B. xsinx C. xcosx D.…
Exercise 7.11- integrate _0^pi /2 cos^2xdx By using the properties of definite integrals,…
- integrate _0^pi /2 root sinx/root sinx + root cosx dx By using the properties of…
- integrate _0^pi /2 sin^3/2 xdx/sin^3/2 x+cos^3/2 x dx By using the properties of…
- integrate _0^pi /2 cos^5xdx/sin^5x+cos^5x By using the properties of definite…
- integrate _-5^5 |x+2|dx By using the properties of definite integrals, evaluate…
- integrate _2^8 |x-5|dx By using the properties of definite integrals, evaluate…
- integrate _0^1z (1-x)^n dx By using the properties of definite integrals,…
- integrate _0^pi /4 log (1+tanx) dx By using the properties of definite…
- integrate _0^2x root 2-xdx By using the properties of definite integrals,…
- integrate _0^pi /2 (2logsinx-logsin2x) dx By using the properties of definite…
- integrate _ - pi /2^pi /2 sin^2xdx By using the properties of definite…
- integrate _0^pi xdx/1+sinx By using the properties of definite integrals,…
- integrate _ - pi /2^pi /2 sin^7xdx By using the properties of definite…
- By using the properties of definite integrals, evaluate the integrals integrate…
- integrate _0^pi /2 sinx-cosx/1+sinxcosxdx By using the properties of definite…
- integrate _0^pi log (1+cosx) dx By using the properties of definite integrals,…
- integrate _0^a root x/root x + root a-x dx By using the properties of definite…
- integrate _0^4 |x-1|dx By using the properties of definite integrals, evaluate…
- Show that integrate _0^af (x) g (x) dx = 2 integrate _0^af (x) dx_s if f and g…
- The value of integrate _ - pi /2^pi /2 (x^3 + xcosx+tan^3x+1) dx A. 0 B. 2 C.…
- The value of integrate _0^pi /2 log (4+3sinx/4+3cosx) dxjs A. 2 B. 3/4 C. 0 D.…
Miscellaneous Exercise- Integrate the function: 1/x-x^3
- Integrate the function: 1/root x+a + root x+b
- Integrate the function: 1/x root ax-x^2 [: putx = a/t]
- Integrate the function: 1/x^2 (x^4 + 1)^3/4
- Integrate the function: 1/x^1/2 + x^1/3 [hintegrate 1/x^1/2 + x^1/3 = 1/x^1/3…
- Integrate the function: 5x/(x+1) (x^2 + 9)
- Integrate the function: sinx/sin (x-a)
- Integrate the function: e^5logx-e^4logx/e^3logx-e^2logx
- Integrate the function: cosx/root 4-sin^2x
- Integrate the function:
- Integrate the function: 1/cos (x+a) cos (x+b)
- Integrate the function: x^3/root 1-x^8
- Integrate the function: e^x/(1+e^x) (2+e^x)
- Integrate the function: 1/(x^2 + 1) (x^2 + 4)
- Integrate the function: cos^3xe^logsinx
- Integrate the function: e^3logx (x^4 + 1)^-1
- Integrate the function: f^there there eξ sts (ax+b) [f (ax+b)]^n
- Integrate the function: 1/root sin^3xsin (x + alpha)
- Integrate the function: sin^-1root x-cos^-1root x/sin^-1root x+cos^-1root x , x…
- Integrate the function: root 1 - root x/1 + root x
- Integrate the function: 2+sin2x/1+cos2xe^x
- Integrate the function: x^2 + x+1/(x+1)^2 (x+2)
- Integrate the function: tan^-1root 1-x/1+x
- Integrate:
- Evaluate the definite integral: integrate _ pi /2^pi e^x (1-sinx/1-cosx) dx…
- Evaluate the definite integral: integrate _0^pi /4 sinxcosx/cos^4x+sin^4xdx…
- Evaluate the definite integral: integrate _0^pi /2 cos^2xdx/cos^2x+4sin^2x…
- Evaluate the definite integral: integrate _ pi /6^pi /3 sinx+cosx/root sin2x dx…
- Evaluate the definite integral: integrate _0^1 dx/root 1+x - root x…
- Evaluate the definite integral: integrate _0^pi /4 sinx+cosx/9+16sin2xdx…
- Evaluate the definite integral: integrate _0^pi /2 sin2xtan^-1 (sinx) dx…
- Evaluate the definite integral: integrate _0^pi xtanx/secx+tanxdx…
- Evaluate the definite integral: integrate _1^4 [|x-1|+|x-2|+|x-3|]dx…
- Prove: integrate _1^3 dx/x^2 (x+1) = 2/3 + log 2/3
- Prove: integrate _0^1xe^x dx = 1
- Prove: integrate _-1^1x^17cos^4xdx = 0
- Prove: integrate _0^pi /2 sin^3xdx = 2/3
- Prove: integrate _0^pi /4 2tan^3xdx = 1-log2
- Prove: integrate _0^1sin^-1xdx = pi /2 - 1
- Evaluate integrate _0^1e^2-3x dx as a limit of a sum.
- integrate dx/e^x + e^-x is equal to Choose the correct answersA. log (e^x -…
- integrate cos2x/(sinx+cosx)^2 dx is equal to Choose the correct answersA.…
- If f (a + b - x) = f (x), then integrate _a^bxf (x) is equal to Choose the…
- The value of integrate _0^1tan^-1 (2x-1/1+x-x^2) dx Choose the correct…
Exercise 7.2- 2x/1+x^2 Integrate the functions.
- (logx)^2/x Integrate the functions.
- 1/x+xlogx Integrate the functions.
- sin x sin (cos x) Integrate the functions.
- Integrate the functions. sin (ax + b) cos (ax + b)
- root ax+b Integrate the functions.
- x root x+2 Integrate the functions.
- x root 1+2x^2 Integrate the functions.
- (4x+2) root x^2 +x+1 Integrate the functions.
- 1/x - root x Integrate the functions.
- x/root x+4 , x0 Integrate the functions.
- (x^3 - 1)^1/x x^5 Integrate the functions.
- x^2/(2+3x^3)^3 Integrate the functions.
- 1/x (logx)^m , x0 , m not equal 1 Integrate the functions.
- x/9-4x^2 Integrate the functions.
- e^2x+3 Integrate the functions.
- x/e^x^2 Integrate the functions.
- e^tan^-1x/1+x^2 Integrate the functions.
- e^2x - 1/e^2x + 1 Integrate the functions.
- e^2x - e^-2x/e^2x + e^-2x Integrate the functions.
- tan^2 (2x - 3) Integrate the functions.
- sec^2 (7 - 4x) Integrate the functions.
- sin^-1x/root 1-x^2 Integrate the functions.
- 2cosx-3sinx/6cosx+4sinx Integrate the functions.
- 1/cos^2x (1-tanx)^2 Integrate the functions.
- cosroot x/root x Integrate the functions.
- root sin2x cos2x Integrate the functions.
- cosx/root 1+sinx Integrate the functions.
- cot x log sin x Integrate the functions.
- sinx/1+cosx Integrate the functions.
- sinx/(1+cosx)^2 Integrate the functions.
- 1/1+cotx Integrate the functions.
- 1/1-tanx Integrate the functions.
- root tanx/sinxcosx Integrate the functions.
- (1+logx)^2/x Integrate the functions.
- (x+1) (x+logx)^2/x Integrate the functions.
- x^3sin (tan^-1x^4)/1+x^8 Integrate the functions.
- Choose the correct answer: A. 10x x^10 + C B. 10x + x^10 + C C. (10x x^10)1 + C…
- integrate dx/sin^2xcos^2x equalsA. tan x + cot x + C B. tan x - cot x + C C.…
Exercise 7.3- sin^2 (2x+5) Find the integrals of the functions.
- cos2xcos4xcos6x Find the integrals of the functions.
- sin3xcos4x Find the integrals of the functions.
- sin^3 (2x+1) Find the integrals of the functions.
- sin^3xcos^3x Find the integrals of the functions.
- sinxsin2xsin3x Find the integrals of the functions.
- sin4xsin8x Find the integrals of the functions.
- 1-cos/1+cos Find the integrals of the functions.
- cosx/1+cosx Find the integrals of the functions.
- sin^4x Find the integrals of the functions.
- cos^42x Find the integrals of the functions.
- sin^2x/1+cosx Find the integrals of the functions.
- cos2x-cos2alpha /cosx-cosalpha Find the integrals of the functions.…
- cosx-sinx/1+sin2x Find the integrals of the functions.
- tan^32xsec2x Find the integrals of the functions.
- tan^4x Find the integrals of the functions.
- sin^3x+cos^3x/sin^2xcos^2x Find the integrals of the functions.
- cos2x+2sin^2x/cos^2x Find the integrals of the functions.
- 1/sinxcos^3x Find the integrals of the functions.
- cos2x/(cosx+sinx)^2 Find the integrals of the functions.
- sin^-1 (cosx) Find the integrals of the functions.
- 1/cos (x-a) cos (x-b) Find the integrals of the functions.
- integrate sin^2x-cos^2x/sin^2xcos^2xdx A. tanx+cotx+c B. tanx+cosecx+c C.…
- integrate e^x (1+x)/cos^2 (e^xx) A. -cot (ex^4) + c B. tan (e^x) + c C. tan…
Exercise 7.4- 3x^2/x^6 + 1 Integrate the functions.
- 1/root 1+4x^2 Integrate the functions.
- 1/root (2-x)^2 + 1 Integrate the functions.
- 1/root 9-25x^2 Integrate the functions.
- 3x/1+2x^4 Integrate the functions.
- x^2/1-x^6 Integrate the functions.
- x-1/root x^2 - 1 Integrate the functions.
- x^2/root x^6 + a^6 Integrate the functions.
- sec^2x/root tan^2x+4 Integrate the functions.
- 1/root x^2 + 2x+2 Integrate the functions.
- 1/9x^2 + 6x+5 Integrate the functions.
- 1/root 7-6x-x^2 Integrate the functions.
- 1/root (x-1) (x-2) Integrate the functions.
- 1/root 8+3x-x^2 Integrate the functions.
- 1/root (x-a) (x-b) Integrate the functions.
- 4x+1/root 2x^2 + x-3 Integrate the functions.
- x+2/root x^2 - 1 Integrate the functions.
- 5x-2/1+2x+3x^2 Integrate the functions.
- 6x+7/root (x-5) (x-4) Integrate the functions.
- x+2/root 4x-x^2 Integrate the functions.
- x+2/root x^2 + 2x+3 Integrate the functions.
- x+3/x^2 - 2x-5 Integrate the functions.
- 5x+3/root x^2 + 4x+10 Integrate the functions.
- Choose the correct answer: integrate dx/x^2 + 2x+2 A. xtan^-1 (x+1) + c B.…
- Choose the correct answer: integrate dx/root 9x-4x^2 A. 1/9 sin^-1 (9x-8/8) + c…
Exercise 7.5- x/(x+1) (x+2) Integrate the rational functions.
- 1/x^2 - 9 Integrate the rational functions.
- 3x-1/(x-1) (x-2) (x-3) Integrate the rational functions.
- x/(x-1) (x-2) (x-3) Integrate the rational functions.
- 2x/x^2 + 3x+2 Integrate the rational functions.
- 1-x^2/x (1-2x) Integrate the rational functions.
- x/(x^2 + 1) (x-1) Integrate the rational functions.
- x/(x-1)^2 (x+2) Integrate the rational functions.
- 3x+5/x^3 - x^2 - x+1 Integrate the rational functions.
- 2x-3/(x^2 - 1) (2x+3) Integrate the rational functions.
- 5x/(x+1) (x^2 - 4) Integrate the rational functions.
- x^3 + x+1/x^2 - 1 Integrate the rational functions.
- 2/(1-x) (1+x^2) Integrate the rational functions.
- 3x-1/(x+2)^2 Integrate the rational functions.
- 1/x^4 - 1 Integrate the rational functions.
- 1/x (x^n + 1) [Hint: multiply numerator and denominator by xn-1 and put xn=t]…
- cosx/(1-sinx) (2-sinx) [: x = t] Integrate the rational functions.…
- (x^2 + 1) (x^2 + 2)/(x^2 + 3) (x^2 + 4) Integrate the rational functions.…
- 2x/(x^2 + 1) (x^2 + 3) Integrate the rational functions.
- 1/x (x^4 - 1) Integrate the rational functions.
- 1/(6^x - 1) [Hint: Put ex = t] Integrate the rational functions.
- Choose the correct answer integrate xdx/(x-1) (x-2) A. log| (x-1)^2/x-2|+c B.…
- Integrate the rational functions.A. log|x| - 1/2 log (x^2 + 1) + c B. log|x| +…
Exercise 7.6- xsinx Integrate the functions.
- xsin3x Integrate the functions.
- x^2e^x Integrate the functions.
- xlogx Integrate the functions.
- xlog2x Integrate the functions.
- x^2logx Integrate the functions.
- xsin^-1x Integrate the functions.
- xtan^-1x Integrate the functions.
- xcos^-1x Integrate the functions.
- (sin^-1x)^2 Integrate the functions.
- xcos^-1x/root 1-x^2 Integrate the functions.
- xsec^2x Integrate the functions.
- tan^-1x Integrate the functions.
- x (logx)^2 Integrate the functions.
- (x^2 + 1) logx Integrate the functions.
- e^x (sinx+cosx) Integrate the functions.
- xe^x/(1+x)^2 Integrate the functions.
- e^x (1+sinx/1+cosx) Integrate the functions.
- e^x (1/x - 1/x^2) Integrate the functions.
- (x-3) e^x/(x-1)^3 Integrate the functions.
- e^2xsinx Integrate the functions.
- sin^-1 (2x/1+x^2) Integrate the functions.
- integrate x^2e^x^3 dxequdls Choose the correct answer:A. 1/3 e^x^3 + c B. 1/3…
- integrate e^xsecx (1+tanx) dx Choose the correct answer:A. e^xcosx+c B.…
Exercise 7.7- Integrate : root 4-x^2
- Integrate : root 1-4x^2
- Integrate : root x^2 + 4x+6
- Integrate : root x^2 + 4x+1
- Integrate : root 1-4x-x^2
- Integrate : root x^2 + 4x-5
- Integrate : root 1+3x-x^2
- Integrate : root x^2 + 3x
- Integrate : root 1 + x^2/9
- integrate root 1+x^2 dx is equal to Choose the correct answerA. x/2 root 1+x^2…
- integrate root x^2 - 8x+7 dx is equal to A. 1/2 (x-4) root x^2 - 2x+7 +…
Exercise 7.8- integrate _a^bxdx Evaluate the following definite integrals as limit of sums.…
- integrate _0^5 (x+1) dx Evaluate the following definite integrals as limit of…
- integrate _2^3x^2 dx Evaluate the following definite integrals as limit of sums.…
- integrate _1^4 (x^2 - x) dx Evaluate the following definite integrals as limit…
- integrate _-1^1e^x dx Evaluate the following definite integrals as limit of…
- integrate _0^4 (x+e^2x) dx Evaluate the following definite integrals as limit of…
Exercise 7.9- Evaluate integrate _-1^1 (x+1) dx
- Evaluate integrate _2^3 1/x dx
- Evaluate integrate _1^2 (4x^3 -5x^2 +6x+9) dx
- Evaluate integrate _0^pi /4 sin2xdx
- Evaluate integrate _0^pi /2 cos2xdx
- Evaluate integrate _4^5e^x dx
- Evaluate integrate _0^pi /4 tanxdx
- Evaluate integrate _ pi /6^pi /4 cosecxdx
- Evaluate integrate _0^1 dx/root 1-x^2
- Evaluate integrate _0^1 dx/1+x^2
- Evaluate integrate _2^3 dx/x^2 - 1
- Evaluate integrate _0^pi /2 cos^2xdx
- Evaluate integrate _2^3 xdx/x^2 + 1
- Evaluate integrate _0^1 2x+3/5x^2 + 1 dx
- Evaluate integrate _0^1xe^x^2 dx
- Evaluate integrate _1^2 5x^2/x^2 + 4x+3
- Evaluate integrate _0^pi /1 (2sec^2x+x^3 + 2) dx
- Evaluate integrate _0^pi (sin^2 x/2 - cos^2 x/2) dx
- Evaluate integrate _0^2 6x+3/x^2 + 4 dx
- Evaluate integrate _0^1 (xe^x + sin pi x/4) dx
- integrate _1^root 3 dx/x^2 + 1 equalsA. π/3 B. 2π/3 C. π/6 D. π/12…
- integrate dx/4+9x^2 equalsA. π/6 B. π/12 C. π/24 D. π/4
- sin 2x Find an anti-derivative (or integral) of the following functions by the…
- cos 3x Find an anti-derivative (or integral) of the following functions by the…
- e2x Find an anti-derivative (or integral) of the following functions by the…
- (ax + b)^2 Find an anti-derivative (or integral) of the following functions by…
- sin 2x - 4 e3x Find an anti-derivative (or integral) of the following functions…
- Find the following integrals. integrate (4e^3x + 1) dx
- integrate x^2 (1- 1/x^2) dx Find the following integrals.
- integrate (ax^2 + bx+c) dx Find the following integrals.
- integrate 2x^2 + e^x dx Find the following integrals.
- integrate (root x - 1/root x)^2 dx Find the following integrals.
- integrate x^3 + 5x^2 - 4/x^2 dx Find the following integrals.
- integrate x^3 + 3x+4/root x dx Find the following integrals.
- integrate x^3 - x^2 + x-1/x-1dx Find the following integrals.
- integrate (1-x) root xdx Find the following integrals.
- integrate root x (3x^2 + 2x+3) dx Find the following integrals.
- integrate (2x-3cosx+e^x) dx Find the following integrals.
- integrate (2x^2 - 3sinx+5 root x) dx Find the following integrals.…
- integrate secx (secx+tanx) dx Find the following integrals.
- integrate sec^2x/cosec^2xdx Find the following integrals.
- integrate 2-3sinx/cos^2xdx Find the following integrals.
- The anti-derivative of (root x + 1/root x) equalsA. 1/3 x^1/3 + 2x^1/2 + c B.…
- If d/dx f (x) = 4x^3 - 3/x^4 such that f(2) = 0. Then f(x) isA. x^4 + 1/x^3 -…
- Evaluate the integrals using substitution. integrate _0^1 x/x^2 + 1 dx…
- integrate _0^pi /2 root sinphi cos^5phi d phi Evaluate the integrals using…
- integrate _0^1sin^-1 (2x/1+x^2) dx Evaluate the integrals using substitution.…
- integrate _0^2root x+2 (putx+2 = t^2) Evaluate the integrals using substitution.…
- integrate _0^pi /2 sinx/1+cos^2xdx Evaluate the integrals using substitution.…
- integrate _0^2 dx/x+4-x^2 Evaluate the integrals using substitution.…
- integrate _-1^1 dx/x^2 + 2x+5 Evaluate the integrals using substitution.…
- integrate _1^2 (1/x - 1/2x^2) e^2x dx Evaluate the integrals using substitution.…
- The value of the integral integrate _ 1/3^1 (x-x^3)^1/3/x^4 dx isA. 6 B. 0 C. 3…
- If f (x) = integrate _0^xtsintegrate dt then f'(x) isA. B. xsinx C. xcosx D.…
- integrate _0^pi /2 cos^2xdx By using the properties of definite integrals,…
- integrate _0^pi /2 root sinx/root sinx + root cosx dx By using the properties of…
- integrate _0^pi /2 sin^3/2 xdx/sin^3/2 x+cos^3/2 x dx By using the properties of…
- integrate _0^pi /2 cos^5xdx/sin^5x+cos^5x By using the properties of definite…
- integrate _-5^5 |x+2|dx By using the properties of definite integrals, evaluate…
- integrate _2^8 |x-5|dx By using the properties of definite integrals, evaluate…
- integrate _0^1z (1-x)^n dx By using the properties of definite integrals,…
- integrate _0^pi /4 log (1+tanx) dx By using the properties of definite…
- integrate _0^2x root 2-xdx By using the properties of definite integrals,…
- integrate _0^pi /2 (2logsinx-logsin2x) dx By using the properties of definite…
- integrate _ - pi /2^pi /2 sin^2xdx By using the properties of definite…
- integrate _0^pi xdx/1+sinx By using the properties of definite integrals,…
- integrate _ - pi /2^pi /2 sin^7xdx By using the properties of definite…
- By using the properties of definite integrals, evaluate the integrals integrate…
- integrate _0^pi /2 sinx-cosx/1+sinxcosxdx By using the properties of definite…
- integrate _0^pi log (1+cosx) dx By using the properties of definite integrals,…
- integrate _0^a root x/root x + root a-x dx By using the properties of definite…
- integrate _0^4 |x-1|dx By using the properties of definite integrals, evaluate…
- Show that integrate _0^af (x) g (x) dx = 2 integrate _0^af (x) dx_s if f and g…
- The value of integrate _ - pi /2^pi /2 (x^3 + xcosx+tan^3x+1) dx A. 0 B. 2 C.…
- The value of integrate _0^pi /2 log (4+3sinx/4+3cosx) dxjs A. 2 B. 3/4 C. 0 D.…
- Integrate the function: 1/x-x^3
- Integrate the function: 1/root x+a + root x+b
- Integrate the function: 1/x root ax-x^2 [: putx = a/t]
- Integrate the function: 1/x^2 (x^4 + 1)^3/4
- Integrate the function: 1/x^1/2 + x^1/3 [hintegrate 1/x^1/2 + x^1/3 = 1/x^1/3…
- Integrate the function: 5x/(x+1) (x^2 + 9)
- Integrate the function: sinx/sin (x-a)
- Integrate the function: e^5logx-e^4logx/e^3logx-e^2logx
- Integrate the function: cosx/root 4-sin^2x
- Integrate the function:
- Integrate the function: 1/cos (x+a) cos (x+b)
- Integrate the function: x^3/root 1-x^8
- Integrate the function: e^x/(1+e^x) (2+e^x)
- Integrate the function: 1/(x^2 + 1) (x^2 + 4)
- Integrate the function: cos^3xe^logsinx
- Integrate the function: e^3logx (x^4 + 1)^-1
- Integrate the function: f^there there eξ sts (ax+b) [f (ax+b)]^n
- Integrate the function: 1/root sin^3xsin (x + alpha)
- Integrate the function: sin^-1root x-cos^-1root x/sin^-1root x+cos^-1root x , x…
- Integrate the function: root 1 - root x/1 + root x
- Integrate the function: 2+sin2x/1+cos2xe^x
- Integrate the function: x^2 + x+1/(x+1)^2 (x+2)
- Integrate the function: tan^-1root 1-x/1+x
- Integrate:
- Evaluate the definite integral: integrate _ pi /2^pi e^x (1-sinx/1-cosx) dx…
- Evaluate the definite integral: integrate _0^pi /4 sinxcosx/cos^4x+sin^4xdx…
- Evaluate the definite integral: integrate _0^pi /2 cos^2xdx/cos^2x+4sin^2x…
- Evaluate the definite integral: integrate _ pi /6^pi /3 sinx+cosx/root sin2x dx…
- Evaluate the definite integral: integrate _0^1 dx/root 1+x - root x…
- Evaluate the definite integral: integrate _0^pi /4 sinx+cosx/9+16sin2xdx…
- Evaluate the definite integral: integrate _0^pi /2 sin2xtan^-1 (sinx) dx…
- Evaluate the definite integral: integrate _0^pi xtanx/secx+tanxdx…
- Evaluate the definite integral: integrate _1^4 [|x-1|+|x-2|+|x-3|]dx…
- Prove: integrate _1^3 dx/x^2 (x+1) = 2/3 + log 2/3
- Prove: integrate _0^1xe^x dx = 1
- Prove: integrate _-1^1x^17cos^4xdx = 0
- Prove: integrate _0^pi /2 sin^3xdx = 2/3
- Prove: integrate _0^pi /4 2tan^3xdx = 1-log2
- Prove: integrate _0^1sin^-1xdx = pi /2 - 1
- Evaluate integrate _0^1e^2-3x dx as a limit of a sum.
- integrate dx/e^x + e^-x is equal to Choose the correct answersA. log (e^x -…
- integrate cos2x/(sinx+cosx)^2 dx is equal to Choose the correct answersA.…
- If f (a + b - x) = f (x), then integrate _a^bxf (x) is equal to Choose the…
- The value of integrate _0^1tan^-1 (2x-1/1+x-x^2) dx Choose the correct…
- 2x/1+x^2 Integrate the functions.
- (logx)^2/x Integrate the functions.
- 1/x+xlogx Integrate the functions.
- sin x sin (cos x) Integrate the functions.
- Integrate the functions. sin (ax + b) cos (ax + b)
- root ax+b Integrate the functions.
- x root x+2 Integrate the functions.
- x root 1+2x^2 Integrate the functions.
- (4x+2) root x^2 +x+1 Integrate the functions.
- 1/x - root x Integrate the functions.
- x/root x+4 , x0 Integrate the functions.
- (x^3 - 1)^1/x x^5 Integrate the functions.
- x^2/(2+3x^3)^3 Integrate the functions.
- 1/x (logx)^m , x0 , m not equal 1 Integrate the functions.
- x/9-4x^2 Integrate the functions.
- e^2x+3 Integrate the functions.
- x/e^x^2 Integrate the functions.
- e^tan^-1x/1+x^2 Integrate the functions.
- e^2x - 1/e^2x + 1 Integrate the functions.
- e^2x - e^-2x/e^2x + e^-2x Integrate the functions.
- tan^2 (2x - 3) Integrate the functions.
- sec^2 (7 - 4x) Integrate the functions.
- sin^-1x/root 1-x^2 Integrate the functions.
- 2cosx-3sinx/6cosx+4sinx Integrate the functions.
- 1/cos^2x (1-tanx)^2 Integrate the functions.
- cosroot x/root x Integrate the functions.
- root sin2x cos2x Integrate the functions.
- cosx/root 1+sinx Integrate the functions.
- cot x log sin x Integrate the functions.
- sinx/1+cosx Integrate the functions.
- sinx/(1+cosx)^2 Integrate the functions.
- 1/1+cotx Integrate the functions.
- 1/1-tanx Integrate the functions.
- root tanx/sinxcosx Integrate the functions.
- (1+logx)^2/x Integrate the functions.
- (x+1) (x+logx)^2/x Integrate the functions.
- x^3sin (tan^-1x^4)/1+x^8 Integrate the functions.
- Choose the correct answer: A. 10x x^10 + C B. 10x + x^10 + C C. (10x x^10)1 + C…
- integrate dx/sin^2xcos^2x equalsA. tan x + cot x + C B. tan x - cot x + C C.…
- sin^2 (2x+5) Find the integrals of the functions.
- cos2xcos4xcos6x Find the integrals of the functions.
- sin3xcos4x Find the integrals of the functions.
- sin^3 (2x+1) Find the integrals of the functions.
- sin^3xcos^3x Find the integrals of the functions.
- sinxsin2xsin3x Find the integrals of the functions.
- sin4xsin8x Find the integrals of the functions.
- 1-cos/1+cos Find the integrals of the functions.
- cosx/1+cosx Find the integrals of the functions.
- sin^4x Find the integrals of the functions.
- cos^42x Find the integrals of the functions.
- sin^2x/1+cosx Find the integrals of the functions.
- cos2x-cos2alpha /cosx-cosalpha Find the integrals of the functions.…
- cosx-sinx/1+sin2x Find the integrals of the functions.
- tan^32xsec2x Find the integrals of the functions.
- tan^4x Find the integrals of the functions.
- sin^3x+cos^3x/sin^2xcos^2x Find the integrals of the functions.
- cos2x+2sin^2x/cos^2x Find the integrals of the functions.
- 1/sinxcos^3x Find the integrals of the functions.
- cos2x/(cosx+sinx)^2 Find the integrals of the functions.
- sin^-1 (cosx) Find the integrals of the functions.
- 1/cos (x-a) cos (x-b) Find the integrals of the functions.
- integrate sin^2x-cos^2x/sin^2xcos^2xdx A. tanx+cotx+c B. tanx+cosecx+c C.…
- integrate e^x (1+x)/cos^2 (e^xx) A. -cot (ex^4) + c B. tan (e^x) + c C. tan…
- 3x^2/x^6 + 1 Integrate the functions.
- 1/root 1+4x^2 Integrate the functions.
- 1/root (2-x)^2 + 1 Integrate the functions.
- 1/root 9-25x^2 Integrate the functions.
- 3x/1+2x^4 Integrate the functions.
- x^2/1-x^6 Integrate the functions.
- x-1/root x^2 - 1 Integrate the functions.
- x^2/root x^6 + a^6 Integrate the functions.
- sec^2x/root tan^2x+4 Integrate the functions.
- 1/root x^2 + 2x+2 Integrate the functions.
- 1/9x^2 + 6x+5 Integrate the functions.
- 1/root 7-6x-x^2 Integrate the functions.
- 1/root (x-1) (x-2) Integrate the functions.
- 1/root 8+3x-x^2 Integrate the functions.
- 1/root (x-a) (x-b) Integrate the functions.
- 4x+1/root 2x^2 + x-3 Integrate the functions.
- x+2/root x^2 - 1 Integrate the functions.
- 5x-2/1+2x+3x^2 Integrate the functions.
- 6x+7/root (x-5) (x-4) Integrate the functions.
- x+2/root 4x-x^2 Integrate the functions.
- x+2/root x^2 + 2x+3 Integrate the functions.
- x+3/x^2 - 2x-5 Integrate the functions.
- 5x+3/root x^2 + 4x+10 Integrate the functions.
- Choose the correct answer: integrate dx/x^2 + 2x+2 A. xtan^-1 (x+1) + c B.…
- Choose the correct answer: integrate dx/root 9x-4x^2 A. 1/9 sin^-1 (9x-8/8) + c…
- x/(x+1) (x+2) Integrate the rational functions.
- 1/x^2 - 9 Integrate the rational functions.
- 3x-1/(x-1) (x-2) (x-3) Integrate the rational functions.
- x/(x-1) (x-2) (x-3) Integrate the rational functions.
- 2x/x^2 + 3x+2 Integrate the rational functions.
- 1-x^2/x (1-2x) Integrate the rational functions.
- x/(x^2 + 1) (x-1) Integrate the rational functions.
- x/(x-1)^2 (x+2) Integrate the rational functions.
- 3x+5/x^3 - x^2 - x+1 Integrate the rational functions.
- 2x-3/(x^2 - 1) (2x+3) Integrate the rational functions.
- 5x/(x+1) (x^2 - 4) Integrate the rational functions.
- x^3 + x+1/x^2 - 1 Integrate the rational functions.
- 2/(1-x) (1+x^2) Integrate the rational functions.
- 3x-1/(x+2)^2 Integrate the rational functions.
- 1/x^4 - 1 Integrate the rational functions.
- 1/x (x^n + 1) [Hint: multiply numerator and denominator by xn-1 and put xn=t]…
- cosx/(1-sinx) (2-sinx) [: x = t] Integrate the rational functions.…
- (x^2 + 1) (x^2 + 2)/(x^2 + 3) (x^2 + 4) Integrate the rational functions.…
- 2x/(x^2 + 1) (x^2 + 3) Integrate the rational functions.
- 1/x (x^4 - 1) Integrate the rational functions.
- 1/(6^x - 1) [Hint: Put ex = t] Integrate the rational functions.
- Choose the correct answer integrate xdx/(x-1) (x-2) A. log| (x-1)^2/x-2|+c B.…
- Integrate the rational functions.A. log|x| - 1/2 log (x^2 + 1) + c B. log|x| +…
- xsinx Integrate the functions.
- xsin3x Integrate the functions.
- x^2e^x Integrate the functions.
- xlogx Integrate the functions.
- xlog2x Integrate the functions.
- x^2logx Integrate the functions.
- xsin^-1x Integrate the functions.
- xtan^-1x Integrate the functions.
- xcos^-1x Integrate the functions.
- (sin^-1x)^2 Integrate the functions.
- xcos^-1x/root 1-x^2 Integrate the functions.
- xsec^2x Integrate the functions.
- tan^-1x Integrate the functions.
- x (logx)^2 Integrate the functions.
- (x^2 + 1) logx Integrate the functions.
- e^x (sinx+cosx) Integrate the functions.
- xe^x/(1+x)^2 Integrate the functions.
- e^x (1+sinx/1+cosx) Integrate the functions.
- e^x (1/x - 1/x^2) Integrate the functions.
- (x-3) e^x/(x-1)^3 Integrate the functions.
- e^2xsinx Integrate the functions.
- sin^-1 (2x/1+x^2) Integrate the functions.
- integrate x^2e^x^3 dxequdls Choose the correct answer:A. 1/3 e^x^3 + c B. 1/3…
- integrate e^xsecx (1+tanx) dx Choose the correct answer:A. e^xcosx+c B.…
- Integrate : root 4-x^2
- Integrate : root 1-4x^2
- Integrate : root x^2 + 4x+6
- Integrate : root x^2 + 4x+1
- Integrate : root 1-4x-x^2
- Integrate : root x^2 + 4x-5
- Integrate : root 1+3x-x^2
- Integrate : root x^2 + 3x
- Integrate : root 1 + x^2/9
- integrate root 1+x^2 dx is equal to Choose the correct answerA. x/2 root 1+x^2…
- integrate root x^2 - 8x+7 dx is equal to A. 1/2 (x-4) root x^2 - 2x+7 +…
- integrate _a^bxdx Evaluate the following definite integrals as limit of sums.…
- integrate _0^5 (x+1) dx Evaluate the following definite integrals as limit of…
- integrate _2^3x^2 dx Evaluate the following definite integrals as limit of sums.…
- integrate _1^4 (x^2 - x) dx Evaluate the following definite integrals as limit…
- integrate _-1^1e^x dx Evaluate the following definite integrals as limit of…
- integrate _0^4 (x+e^2x) dx Evaluate the following definite integrals as limit of…
- Evaluate integrate _-1^1 (x+1) dx
- Evaluate integrate _2^3 1/x dx
- Evaluate integrate _1^2 (4x^3 -5x^2 +6x+9) dx
- Evaluate integrate _0^pi /4 sin2xdx
- Evaluate integrate _0^pi /2 cos2xdx
- Evaluate integrate _4^5e^x dx
- Evaluate integrate _0^pi /4 tanxdx
- Evaluate integrate _ pi /6^pi /4 cosecxdx
- Evaluate integrate _0^1 dx/root 1-x^2
- Evaluate integrate _0^1 dx/1+x^2
- Evaluate integrate _2^3 dx/x^2 - 1
- Evaluate integrate _0^pi /2 cos^2xdx
- Evaluate integrate _2^3 xdx/x^2 + 1
- Evaluate integrate _0^1 2x+3/5x^2 + 1 dx
- Evaluate integrate _0^1xe^x^2 dx
- Evaluate integrate _1^2 5x^2/x^2 + 4x+3
- Evaluate integrate _0^pi /1 (2sec^2x+x^3 + 2) dx
- Evaluate integrate _0^pi (sin^2 x/2 - cos^2 x/2) dx
- Evaluate integrate _0^2 6x+3/x^2 + 4 dx
- Evaluate integrate _0^1 (xe^x + sin pi x/4) dx
- integrate _1^root 3 dx/x^2 + 1 equalsA. π/3 B. 2π/3 C. π/6 D. π/12…
- integrate dx/4+9x^2 equalsA. π/6 B. π/12 C. π/24 D. π/4
Exercise 7.1
Question 1.Find an anti-derivative (or integral) of the following functions by the method of inspection.
sin 2x
Answer:Method: To find the anti derivative of a function by inspection
Steps: 1. In this method we look for a function whose derivative is the given function. For Example: if we need to find anti derivative of x2, we know that derivative of x3 is 3x2. Therefore, the variable terms comes out to be the same.
2. After that balance out the coefficients of variables by dividing and multiplying suitable terms. From above example if [we divide x3 by 3 we will get the answer as x2. Hence, we can say that anti derivative of x2 is x3/3.
Now, similarly,
We know that ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the anti-derivative of sin2x is ![](data:image/png;base64,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)
Question 2.Find an anti-derivative (or integral) of the following functions by the method of inspection.
cos 3x
Answer:We know that ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the anti-derivative of cos3x is
.
Question 3.Find an anti-derivative (or integral) of the following functions by the method of inspection.
e2x
Answer:We know that ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the anti-derivative of
is
.
Question 4.Find an anti-derivative (or integral) of the following functions by the method of inspection.
(ax + b)2
Answer:We know that ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Therefore, the anti-derivative of
is
.
Question 5.Find an anti-derivative (or integral) of the following functions by the method of inspection.
sin 2x – 4 e3x
Answer:We know that
![](data:image/png;base64,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)
Therefore, the anti-derivative of sin2x is
…(1)
Also,
![](data:image/png;base64,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)
Therefore, the anti-derivative of
is
…(2)
From (1) and (2), we get,
![](data:image/png;base64,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)
= sin 2x – 4e3x
Therefore, the anti-derivative of sin 2x – 4 e3x is
.
Question 6.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 7.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 8.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 9.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 10.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now we know that,
∫xn dx ![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
Question 11.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Separating the terms we get,
![](data:image/png;base64,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)
Applying the formula,
∫xn dx = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer.
Question 12.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Separating the terms we get,
![](data:image/png;base64,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)
Applying the formula,
∫ xn dx = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 13.Find the following integrals.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAAA0CAYAAACZ3pqKAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAQlSURBVHja7Zw9TtxAFMcnPekDwtvlAHhMmyoyFqJNBGtRgbZAyCkotkhh6FaKOEDo6NKkjpRwAk6QFJwAzrCLnz8WZ1l7Z9brmfHsP9K/iUA8v/l55n2MH7u6umIQ1KbgBMg+yJJ/b0jGOMAwewBZQ537zkWyoGPGnKcgind0PvhoNNgIttldZg9/OI7jTQDRccjiKNjhfnQ6hY33b3U+eOTz0wL0Pme3bDu4G4xGG4DCkpjsMuQHjn9+YYoT6AVwmHuP3cwSyIbDwdsgCE9MckIcH2+6zP0DyCyALNsx2GMSB01M28mKo9yqxTUkodHyR9OYzKAYKAyCE5visSgM9vd478aUhEbb8cR7ezcmLCwBz8PLA1sAo+fp9dhfOi3WErKiJmVK4E8LQnaQTcPh8ZbvR59tieHSjHkdICvHBC81skSayhdle7JFyO3JanePorW7VULWVtxkHWRnZ59cz3F+leGhOlQa5GuIvdq2ZxnIouhoR6WPOgdZ3dtGR1++G0yKSn7IeXwUxe91PJAKe2Qh0+GjzkBGqb3rsPu05MD71/UZze5h8lY+Mce9X0XLqIjf6qTLHorfUsiGwy1Re5axqYkPOgFZmgEy9jD7Blb9/LQXuIKt/3W8NF91yYMCeyav/m9BrCljU1MfdAKyIgOcFlAFHJMF9+Y0m9uyp0ngr8pHnYCMjJQpM5DjA86/0XFgQt2pTXuWhUylj4yHbLqtS5QaqGoeXUbvZH+vLbVpz7KQqfRRm5DJ3sFrBFlxZYfaGLPXZihl5zyMlR+PCuyRgUyHj9JLCB77SZB9PPvqtpa9C74ojQLULL5wHnfD6PC/WC6J4SgbVV0fU2VPlhTx38KQKfRRCYJxW8XvPE4XPvJbz8wg+5SBLH4ULyhf4FoyVBHvSWxAgAwSDvbLbNRVHmaTAkAG1YoSlrzrM+7xvRvqWhSFedEe8QLI9H9VBOkRxeV97lynt1PCaD8DLm+LUWacwvbSDaIstqofC8ig6rhrZv3nHZUi/djaFLUOMpHmLWSWJMsgk9kSRcaF86/MhEgloglkY6hbEj0mq6CpyioX9WOXhgyyU1WF1ryA/DRb2BXpxyImgxYelQSe53nf54Ek0o8FZNDcnaz4wIZKGPRNanEk+r7/xfOcHzL9WEAGzcksqXSRxHGUMebli6IHGxzFH2T7sSjGQq0LkEF6IHuZ3QXIpJyJYXqArC2ZNnsCkFkmE2dPdAKyckqKS4uiGZk5H250BjLTxjuZHjcBMgnIikUwYa5rE6mezwHIBCHL7w+lrYMuz+1a99kTxkJWGkswsSWIlZk90fSqDCAT3MmmM8RWNKREt0S/ulrF7A1AtkTgb1OJYd1mTwAyhVrX2ROATKFsmT0ByEw8Hi2aPQHIjI3B7Jo9AcggCJBBgAyyXs8SqBdVW8B4fAAAAABJRU5ErkJggg==)
Answer:![](data:image/png;base64,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)
Now the numerator can be factorized as,
x3 - x2 + x - 1 = x2(x - 1) + 1(x - 1)
x3 - x2 + x - 1 = (x2 + 1)(x - 1)
Now putting this in given integral we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 14.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 15.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALAAAAAkCAYAAAApQLALAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWwSURBVHja7Zy9bts6FICZvdmboPTW7jWTsZ0CRU3asT8y4amNh8AgcG8DaAhaJVuG5gGaqZ3aAvcJbjreJXmCW6B5AvsZ7IqSqDAyKZEUJSsthwMEMSweHn48PD+UwfHxMXDi5LaKM4ITB7D04QCsmIhbGCddAXhuImXPJNjfCUh03y1eNyQi/kMfk53OAWzDG3JQznRE9rwjjJ4ifPS0caO400BLiIfetLEuygDTXdWH4BIAdFXH2zF4be10iAanTRvk5GR0x4fgPN1M6GoYhusO0mqbPYHw69b+Yb8TAA8Q+JwuIJz4JHpYB2Bbig4QPK2ji443YeMkdrjnfx+dnNxxoJYLPR0BGnxeOsBRNFxDve2zuouWHcFWAE68L/S/tQ1SMi7oXw6jaM1BWmGrmJs+gJdte+EmAZ7bAph6QuiN3y5nUfrnDmD1ddL1wrXzrKa8jq34N9lQAFxVJQlNJF7UFsgjb1rxJB0uJarqlYQRNG9QZGcceLs016rjnCQAwx91401b3jc1CpyW6ZOABsFFFrdPkTfeszE29v3XbYQt42AzgABM000PpzRZHYXhaidCAw3bpuyAqUpFgvjw76zqNP+tAR578G3Zrqb6bvr4LwoazYaxDyM6dt2yDh3X9Bk6HjTdoAulxHlTyaOObgLbvk9sG0TPyk5LVSAZ8J0D2FYCl5S07oHvMoDp50Nv+EL4HcOMmOoew3sQG/WA/h2Gw3XPIy+aiJvTkh38tonJq9wzYX8nXtSJjU1YVzdd2zKAVW3fIMBqx4Bq/CuK71TiqtwgGt6IGZk3is74GIFPN72hXilRB5KkixVEjyVeOQfY1H62k1KRbYWAl6wXr3cRYJN5NgZw4XmTvCsXT45Ewf0YzJ8MdNlYJgAf7m/1+YZHnfGXVbngwyab+tfVrWhb3RPzcP/5g7RBFjsGiC6CsbfLADadpzHAZTu/GD5w3a08fsqSs0lZH53ponIkheFoNU2G4A8vGO/aGH9ZABfLhrb0N9WtaFvZ2l8DvJh0F71tRGI40+QwT+JM5qkFcMHFz6VuXRD/Zt70J52ch/HLDbjxtcqQqgBfPztLgASZrcn4JuUvGjMnkIThuklpLJ0zuijqJtD/S5X+NnST2PZAB2BZ7MxCJX6tdOepC/CMu5wjbFRkBpmVAllRFjPxwIlBCLmLEfyQ6rZ4jOmOr1RqW4iZb9joWhD+pJrUyXTT1d+mblW2LQNYlqxV/H+iMk/tKgSDkzPGik75jN5pKNvFwgXTLCmldznEk9cZv+0QQuVWV6b/zER/W+GNzLYygItJqUoVQnWetcpoIojLAGY3yvJaraSeWCeJ4+ImcRymMX6bANPErbiQRedQV38bAJc1lmRJnChUqPTACH9QmadkkvBS9Yjl7vyulAFM4y8Wd14H63BadvlDpyyzYGTon/PfMRm/LYDHHtqjHa6b8epodbuHzthzMv2/1NFfVzdV21atVx7X0v9zHUYO4AM2ju48bQA84yEWxb90MWhsxyuRlGSSeA5dPd8/fGBSlmEG6KHtM/oMOn7SCIDwP15/0/HbADgtmUneTslif1v669aoVWyr2sjIW8fxZxTiZE4bvY9ZC30GNp78M4pGa7rzXNhxFBp+5+tCXJ5MpE0BruaXJxKy2K+slXzz8nn6fHr0EHJ019b4JgAjgP5VsR93H0AoTCdb+uvoJrbt4LRoWxHAskYHjfFzvWMvTsjWox7o/c/a1SbzXBgcYbznIe+dbh+eQWw7plS5zOOkG2KjCaZdxlzcceZvYdh6fUi0q5f1zpUTXWejfp3SKsBdFpOL0k7+jHW6PUfTEl4pcqIuVU2YPxpgtrtdGNFxJ9PCW+O3FmDnhbvuYNp5a/zWAsyShLbeUXOiLgRvvurUD5t021jup6W6djLyb5Q4gJ04cQA7cQA7ceIAduLEAezEiVR+AV9Ew9qCAkh5AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
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)
Question 16.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 17.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 18.Find the following integrals.
![](data:image/png;base64,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)
Answer:
Formulas Used: ∫ sec2x dx = tanx + c and ∫ secx tanx dx = sec x + c
![](data:image/png;base64,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)
Opening the brackets we get,
![](data:image/png;base64,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)
Answer.
Question 19.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= tanx –x +C
Question 20.Find the following integrals.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOgAAAAbCAYAAAB2r8PPAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAbISURBVHja7Vs/b9tGFL/uyR4bPm32Hp00NpNBM3Y8Og1FaGlsDYRA1I4BDUZCe/MQd7e7NF3aAp27OGMX+xMkgP0FIn0Gu/eOPPJ05pFHipIo5wI8IOaf47v3e//fCZ2cnCBDhgzVk4wQDBkyBmrIkKHaGCj99wNQ7Tcf8bkIvM5DLkYWj9BAj7z1ZhOja4TIreMHq3Xd+Olp74mN0SVVxDvgtTsYLBuFWBz8jIGWpA5Bn0Klx0PbD57XdeO+RXY5fy5Bv6MV+3Pv9PTJ964Qi4KfMdASFATdJdLYuFg0RQ98+zlGzetuECx9z8qwqPgZA33sBkr5bqLmZdUGumi1nDHQ+tXyc4tEYoNm3koMfBPL360SmL5jbUEth63+u7ooSp6cTSZRP/ynYKD4a17t0nfaDkZoRDdyT2udEW52fu0NBk/nJUzXtt9WGTV8Gx+EdRy6n7eBMueD0RWvK4nV35sUP9PhnR3+MzfQY5e8ipgX6X4eTRrm6Sz8jrjHr6ZT16LRPA0UeGjb7i8gV+hauzb+ALImTrA9iYG6hAQmys4G/5kaKCjJS4z/arv+m9jbuPYm3ciQKc4UDCXHOA+pAA/h/4NBd9my/NePxUBB1l2r+1q+Zq+gz4h0PpU1UBjDmDR4oQ0UjVSGBvdtJ3ihiKpjBirXTWlplU4dq3qGjVbGovj4WCHtvSLfkgEqs940jBYMFNv+QRn8BoPeU2bg0dxY5Fven7wnnX0XlVEVOqK6Xxf8UZaAVVTWQJU1KU0zKeg33CtDNAuH5eiu0bLPPW+nSYgbyJ48qa3oc2TjQq5jj7ydtbxnMvYxDGtkSti+9ANnlSB0E127k/c49i1Mrpy+tcUBKrPeNIhFP9I5K4Pf+MGOkGfu1MBwOwSfiQ5P7CvAfccmBxB5d468NZfgj6Gcmtfr3lEzVea05MmSEegIl3cBHflNxD9FP9j9orwUxl9jvQcG+jCipJPK+05ioDAcF1MB+Jt3VVntBLwJaRlEXIxb//KTLlGaPBLr2MAh2yxdc/1NkTfdWldQyLhmCyM9VcpozfG0j4IRySbwqfBDsOImQZH1qiYwkLAxh79aTn9L5WR18AsPMtAIKqS4/BrHI3S4yd4T3cIjWhPvg/xjPARcZRkBnyoZldSRIccf7jdQ44ukH/H9IrxE+A/5fnXwz1pvbimuuqYhVxxwNotD6JZvIr5G3A/JRvHf4HnFqB4qCR6BR49TOcHoQxCp56bRS7d+ini5gXUt1/2phVt/yu+q6jqetos86KyXl4IVzWySbyYNOai7qzLQWPGoXEGxgQ/usESZpL4HcpMcpo6MJtWRdc97oaMftcB/ngbKBSnWfqKngZR0xztaE5Uv9ryKCA/fLhvJs/bEjV+3GZBzfaha72HHVDOzyWlGHPv+szi1lCLgpBGUOxKI1K7d3o/TuRIGKsuIp8Cq7AbS0sI6YlnvdfUjj5dJ8E9bbwY1aH6bnn8PzsOmCUlIEcJ650GtojXKqawrzOurtMij+lZWFy9rvWmTmGmUwS/NQJMaFA8hhfX99R/LRtA0GaXpnI6OqAwgxkwxbirCi2otXfzzGoRTqEH1DBTqFHktuRsHINitxrno9YWNH+bVUqAgk3ZIw8aK+1E1Q0xLZbIAyltv2hTVPZUZaJqhpdWXRQxUktFdmoyUOjIYLPMopTbuiL9m5w+t01UZvPC5vuxsMyNozt6ml+KyM634OgvgcP5I9uBEixiVwQtvNMiFE/irFrHei902MUqJ6c2K3TmG5+LWtkO2WYqb1F0PnlFF7fTmSneZ1wnJd8dTk/hboGgCz2mORGe9Kikt4wEZ8XqxDH6ioaWNE1QOUtdAdWQE1yfSkW53V0c/6oD/TA2UHw6I280yUUDjBg/pnHHBQQdSHMMIp5GkNTSeUShn6swvajTI3VpQNKh7+PX4aBflH3hm71KvHtdBrZf/9ILeku56VfYDxBqNdTIx/k+Fj46BhplWqFRwRDJKZ4dcQVkdGta6DE/45o7nNcP5aaKMbEyC0K34W1xdmXPlFnXEd9tviuhInn6Uwp9G5Krxr9Rbg+AgCqo6U8IZRWWDhwnfdhnw4lxJVhoAXpxhiS118ZlGA32J51wt+1z3R8jCaIDN+oRZ1hi/yd7ab+P7MOek/EMbnx+1K7repCTNLdl3IbXy/eNnZfEba3IImIh7Z98IaNoZRochRCuZD9t3N8c7y6HR6Moo0pGfJ9WRLP1Q8PKtBP77Gfh/y8O/ssjJ2t6uu8dSD/NzpcU6lmbwqy1V7K3Nr/AXkQx+j9xADRkyZAzUkCFjoIYMGaoP/Q8BGnl7cheKqQAAAABJRU5ErkJggg==)
= 2tanx – 3secx + C
Question 21.The anti-derivative of
equals
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHsAAAA1CAYAAABhlZRjAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASRSURBVHja7VwxT9tAFL7usAPi2OiOL1k7IeO2MIJwrEyFDFF0qiCSByQctqii/QFMsLV/gEqFkQX+QSX4BclvgPrOOdcJdmInPufOvOFbIkT83nf37nvfOwednZ0hwNsAJAHILujLEXonoHUSNYlhrl/eMvGxn6RnhHBvs3li6Ep0jaArbLaOgewEeNTaICY9CEkntSsdyaYWPmILFshOiY5DtrFFj3Qt42yxAtkp4LqNRdO0D3Q+t4HslKUcI9TTpQyWmuyoWpa58/iZvWrdNrrdBSB7DmS37Krt77q+T/KLr5b72Kj9aLjuopQd7tWXydrWBZA9B7KZYApaoiG85Ln7ohVDZ4HGnt8nu+2T3VZdd7z6oNttLHzE+GfVofthe+FYnwZn6wtxOtt5tiwcxLnU9byOxqH67o4VTZbtfUjY7bmRDVBYjQduF3mse94yJK7kZOtiCQJmJPukuWlgRO5hV5ecbCbYLIx/WdTbyFPBJkEnFa5bDBMDoiY5yFuUxbR1ITQiW7sYJpsFI/1vniu3DPNsnWIYYxSQQ2K2DqPBsKHF1hq5yOPsDo4HdBPsBvJUd90V3YjWLYYEonE7sEljkNPcmR0PQgc4BF0W5Y3neb7OK4Zp4xnrCMVBhqkSTL+MB9lqX6bfX1QMAqzK8ngwvgv5weR+t3nynnVP4mLIVH22TLBBiIGMm6yJyrIzZfv9fJiDyB+ZMYSVN1i0PUauTenG/wVnrxOEHpOcTjXIjlxRkrFAivD7ZccQEc1t7sMT5zxukQaL2tcPMf9T6jky6TPxuWNZX7LuriyJmsbvVy0G/vc22Ql0U/LgaNy4OHeim81do4LxbyHkRK8elB3rJvoQAzF4PM3Omrb0j7aWcX6/ijEExwR6YlpjnMHF/444p1M5aFkwfC7iPrse7BDi2dRbT1L9Yg7suvUV06R7RZId5/erGoOoQrN0Q1LKOHWq+1z1YuMhaRXyVmVILOHeuBU72mKwxPJE+b3tNO3UJL9ftRjYwpxVX8gzG1bRbZ595+vEDtT06GcpLkKk8ftViiF8lgklPBPZ48z9rIb/4Dx8ktV3ztKupfX7VYlBFtnPWTAuCKtS+cbKoKybLdOSndbvVy2GsIzb3s7cy3h0t7M2hHboEl+NEUU7T7LT+P0qxxAKR3asxLh+7NmSWszcyRbvazGzQpQavhr9h6PU3khqB4pIVFq/X+UYuGgUVrYvGpktKhan12gss45hkqmTnwLnD4J7UZeKXxH2e9Mkt6coezKt369yDFHnr4LxdfT5Ma5cx7WGStqlgGIASQCyX7dikKwSk82nOBjdC2eIqVhIWAnJZkRXLecrEySsoXcsfApvg5SQbEZu3azvxTo4mv4UBiCDQBNk6/xTGIAsb4SQ2ndIWInJDi+1IfzXtFufQZWXVY0HNyMeo6M4NqSHpJW4jHcoXXIIPg98ZHnjPoAiZzZDMGKbbZ4K0ITsYMQGZJeO7DiLlF9jHblZCdCc7MEP0fXXyNaFmJnyC/UY38GuLhnZw28mBr44m+VS2lmChL2RMxsAZAOAbICK+AcTkiGj5t+4bwAAAABJRU5ErkJggg==)
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 22.If
such that f(2) = 0. Then f(x) is
A.
B. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHAAAAAxCAYAAAAC5C2CAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAATXSURBVHja7Vw/T9tAFD+YC3OhuWztTo6s7YLCAWWMqDllAjxEkaVCJA9UOGyoQv0AdIFOnTq2UunagX6CDvQLAF8B6L2zHV2MQ2xsx2fnkJ4UJS/w7n6+937vz4EODw+RluKK3gQNoBYNoJbJBJD/THkyrbod/ueSTEXUnSolgLCwjtFYWybVzwiRfy3HmVPVDlenbmCEbvjre4TwDa5tfjJteyaou99uviIYXXC9Wy53VbJ8EqZXeAAtinerVfQXFpkngFHscAyy7n4uQLn1Xt+jCv0lg7PfXqpxkK/rzNoQ37OMlxSj86BeqWLgJkFneQI4yo6jI/PZCsZffVBA3jO6AkABiIT13vp6tIJ+IbJ5NgC+05ojCF3iRqerAczBDseiC9RwXgf1e4y8lQEEPXCxHKi9OGvUAOZkR6eB97j+pa8vAdgN18U31HIWNICK2AH6mFq7QVcZFu/c360BVMYOl6yQi6AuI+gUCA4w1KZpzgJ7tSxjgSv/Sd2FyrmKBjC6HbZtzgCpCTtNLqutb3FXeiXYKiYXlNEtfjL/IUzPzaOjZ6kB6PploMT4eqm9X9MAjrZDnKgG2Sat3lqMfe7CqfTJTioAQsCtU2urD2SA+moAhyT8fK/kuOe/P/y0tuYfO32pxECgw0GjNIBh4JEd0ujsyOU002zOLlfJSfA7oA8VGRH78MNYmRqAYECjYWyPqtdlVcKCv08J+gYbB25cRTu8k9d1S2ghQtiprGub5jyj9fci0X/k5CUG0MtbrgRrCkk+s5Zei6xJpSlXpM1QxQ4otT34XJKBSgyUzfh7GC9+p8xajfQAJV2AMBBylxFPSlS/r4Kobl+qAIoEtLp8EhVA0K+h2nneMauo9kUC0O9vheR8U8EcECrtcUiMBjBDAAGYdrtZW8T4B6ptfpFzFxHvvKA64Ndjxh0NYIYASgH5DmpvwKgYIQeG5byclA0qhQu1WH1DdI9x7c+wkk8cQiDnPrbdfAEb1LTtF1FHDLImLCrb9yQA+83FmOwyTLwCbZA+36uQAhTBviezUK9flXqFI46LCpyAVER1++KuYWgNji4ufgQ3SgxnPUcAb9MW1e2Lu4YHqQMIo3TL6lnP5RmNtGLAuEhCMBUqPYkRLpOnDhajqz5xEfGBx0FILQhhB0UCEOqPTynxFRZAN7fDV/L0FKQVkP9hwo6TkpmByg0iP7PcIK8Nc/lUALO2T6lSmorCc1dnZQUf51Fk1wAmFJg3gTE+0TzVABZLRP5K6Adw96oCGOfew8QB6Bj0jddQnfZITFelCkrg3oMYWko6T1Su0+c1RKX7B3d5jnsMPFz+4C5lBz4hhJKlX3PWJzCkkqSSCxVpWqA06Zcsk9hZrIA9ok8pC6RFqpy+PoDeafPthRlRAHDYyGBpAIzap1Q6Prsu9BpAbBidtf6YIc+xSx8Dx9GnHC+I6L5SqfwGICeKhabZp8zLk/A1vOs/jI9c3CwlgGn2KfMAT6Q23GXCOhjBxwJE/jC2bHt+YlhoVn3K7HNUuGY9eEXMmy26S3I1oVDgZdmnzFqGjd6L9xN4lMKkDln3KbMWd3SDAyi5y/7YfQIWXQyXOYY+5dgYKLfbu7w5Df+eBN4rdR44rj7luEAM1kITT/0VjcRo0QBqALWoI/8BYFjZHbyzErwAAAAASUVORK5CYII=)
C.
D. ![](data:image/png;base64,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)
Solution ||| The correct option is (A).
Answer:It is given that ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Also, It is given that f(2) = 0
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOsAAABxCAYAAAA091TwAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAynSURBVHja7Z09c9vKFYbXrm3X/tCii3tzyTZpPDQ08i0ZG8SoiW0WHA7m5lozKJQR5U6FnP76Nve6SnGT0plYTplC+gPRnZH/gOi/ECs4iw+CML52AZAg9RbvjD2SsFhgnz1nzx6cZW/evGEQBLVfeAgQBFghCAKsEARYIajmAcbYjUA38TwAK9RiUCdWf+eJMH5iTHzenU7v4bkAVqiFckz+g2Gw/3rQfgWsgBVaAw0F+wWwAlYIsAJWaL3WhiTAClihlmvS53u8P3kNWAEr1GK57u59wdgFYAWsUMtlC3Gwvc2PAStghWpYTzb191PHfGRa0997bvBrwApYoYqgOf3+Hy1n+judvycYRd95mQbs0dHolinMv4yOjm4BVsAKVQTVc1GnpjN9VOU6h7tih4vh2ySwU8v8w+PxfofS+IIA015bI8KAdYNhDXNJswafzlbFsgeyBMh0fqjjWpQJRDAuWFXOTrw+/S/QV1Jd7dX5HkejwR2zy/5OsHqTi2jzFhNgVXy5++PHHcHZqRyAW+YncvPiv+O6o9tDwd+K3cOdFLhvpkEu3UlhT0eue3sZ/aA+cNY5y7MkRfe8cP/T3Xsdxs/IkmZMDK10g8kriE0ovoT9c4sNRPydRAZhGRNMsu3Wwzq1xHeM8VnPdp4RYAYzzuNu5P548LDL+Qf6ebyTE6tncca+eP++8v7+C+8M/5oEU1on3v0wGO8/XIrblzMoy95zXLZgPzMx/CXT8rbMqq6TyADQ+zAMdh5NKoZx3rMmlusOHtBE33T7ZIDCtmnZkzYWKs9E9Voj9iVr0AX7iZ/jFnUOuHQD4y7hVZpV9md6b+3kuvcbm3C8SYb6IezDp/mTUsY9ZwB7aIunda77NtkdVekbGQBv4J0FRuJ59Lwd567ZNX7M8vDqvFc5uXPzhNqgJc52l/3KOs/fJ/uh3QjN9HUFNeQNd5h3c+IiazCmWSvZMc7/Fre0f7bNbQ+WGQ3+NGDyLFRNa9XXZCmzAks697wwCVjT7ypPKNKt7pxsYsBHpW+hASBQs96XHC8NwupPwovtB+96lnzXeWuoXEn3gCydd0FdYMM2KRhDAzULft/q8t+SDzTcZ0x/AOkD338Q/Les9V8tLnCOBdS553AQyoFVw0QDWOdBwGDcvc67njCevGsKVjleEpNBFED03nWch/xgQCnxmQ6wiYim7wZmBCDSOlRs3dKttGx3i33KG/QKE9eN1GtrzMR591z12oA1Z/LL8YLm1lUcZF1Pd6wUTcDSoieWbHWt0Wa0GNe1sHnWqAxcadfLC7gUwe8/qOKJKtlG9PA1gCq65+g51LBuBazzZUXV52lpjpX4PaRZ9rTlVJ1BldmWOTxUHaTz2SU9ehr+vOzWhO8yi9O8F1C0rqwaXFJ1Vcvc8xxW9ftOzv60hKEBPXDdB2W3j9ocTNLpW7jsWGWyxkpgjfn/X/OioG+yI6OFgZUysFIInII3RYO5TbCWvecqsGZ4Cldl9kBV4hjLUF19axmse2W8zVoaDbZdZty0D3Tcv6KATBlY/Txc8TK5taMDq+46JIK1pBuscs9VYK3iBuvFMZpTzWvWC3qeVYKNNaxZL9Im94CLi1RYVaPBoQhUSl6Ib0XU5QKXjYLKJAPK4kmsC7LcuiJYl7FmVb3n67JmjY/DpvsWvOeroi3IvJ9VWbNGQdbE/vo8TrPIRdVo8JWMBpewDDoucJkAkz/oxSvRn7yKTyKUk/rEEO/SXlpTieVlI7Y693xdosH+ROrvMuhYPJW+hbGWwLqm5i3TMsU2zT819ax87hb7GnqqSS60GwkrFOiCmmXqM19gyiANrNNesEb5VikWO2vWqktRyD0n1K96z2W9kHWHleDpmc6L6J1r7Cmr9k1+1cTYpcxgsibWYDS6E06e4/GgQ+mtdcc2kuNxm7OP1FdqmzKq/D3WlPhBlUFZJR81ivKWuEZWIgPlxOZZ/rSJJLxWUy8gyEjJdLEL77kog0kxgJf97MXHNm/d0HPUGV9B3/6l0jdKLbQFP/ahjfIHLrmwj5tKhkgCS+2H7fZM+/u0dlc3i0oXuNiqLlisREaHznpIWrUGv/wIgwZ1pAWmPK9r8U0oLQf6feslPqdbEazJT46KkgCyINBNvqC/UZ0gKrnCNecfF33Js4pAUBN/G3gQl/L73JQtDcC6rMBBZ/h+NB3do8+ByMXQsVq0huCmPVV1Txy795w+kdMtsaK69pJJDjV93ePHB/hpk2snVdh0y9Xklar5ZrnQYAI9YM2H5VmwkM/0yVX8e5XAVvDx+cEyX3xQ3eF1Ha5c2hbPKkGtWq4mq1TNN55Ugwn0gBVKuMPepFIxIBRONG3pU97EoVL9IlmqJvn3tGTBB/WAdalyTHNQpbphuJXRBuWVq1GtfpFWqmYhUt7S8i+AFVoL5QW5cqpf/DsL2KYLAQBW6Foqb59Xt/pFVKqmwTI7gBW6dsrLp9auflFjqRrACkFxF1gxKaOo+kWdpWoAKwS90f+IoHT1C+ynAlaopvWqRrkateoXOFoDsEL1wKpYAWMZ1S8AKwRVhDWqflEiGQSwAlaoKVhLfVSvU/0CsAJWaGlr1krVL7BmBaxQPSqK2hZXv0h3nxENBqxQA8orV6Nd/aLGUjWAFYICFZWrqbIWrqNUDWCFoEUrWGu5mmVV7gCs0PV0hWtMDWxbqRrACm2Oda2xXE3bStUAVmjjVFe5mjaVqgGs0Aa7w9XK1bStVA1ghTbcwuqVq2lbqRrACkEQYIUgwApBEGCFIAiwQhBghSAIsEIQBFghCLBCEARYIQgCrBAEWDfwQfhng8rzQfE8IMDaYlAnVn/niTB+QqU9CLC2WPSNpmGwc/9MUcAKAdbWS+ekNAgCrIAVggArYIUAK2CFIMAKWCHAiocAWCHAClghCLACVgiwAlbACgHW9j4Exm7Qob+mYP8gWB+P9ztVK85D0FrDqposH//9JuE53BU735wruqQDkxJ9vBn+P/zZktq/2fQzhtYIVtVk+fD3u5z/U8LDzZNNOx3bdUe3J1bPCvKS/UnCMM571sRy3cEDIexp0+0PBX8bts3F8O3IdW8DjA2DNW4BykglWZ4GkTy+nvEZF/ax4xzeVbmvVbnSKr+/Px487HB2Rn3s2c6zyMo7zl2za/won9OW+ampCYruV67Rg0nw6Gh0a7vLfmWd4XtY2A2Dlc7q5P3JnuqLLQri+EcBss90yK7qWSp04G+HdU6WHSBSbXfeRz7LOvJQnoXaIKz+QcaLJ5lHJ5HXeGAy1ACsibVLoaSb5g04erEqwObBSrN7aFF1zu1cF1gnfU6T3BUdnZh3TWE8edcUrPI9JCaD6PnXeGAy1ACsqUGWUuIzFWDzYPVne38Q6wQ+1gFWCaFvVb8UTUi2EAdp11SYWG/k3kMKlNi+2uAAU+A6zSgoUgaqrMEwt6ris2mbLwRnp9Fk0J+8KnPttYA1cDWrACFd5BITadZhxeE9pFl2OuS4zEQCrSGscWC3zOFhkduWBWs023NxajnOoxDgYGCStd0rsjDkmhM0A9d9UMbCVAnO6LZ7aIun1J9VWi/Aeo1hja3DvhadiJ0Ja8YAmruN3/5NhoW5KrNnqrI+L2nZSrXbdljhBm84rPvjxx2yrNy0D7Qta+EAKp7tVdxRlXV5A2vWC+oPZUrVYdmxZr1msKpGg0MRqAYzzuN7hZXc4JQB5LtmxQNoXaLBea59Esom1qwyPsDZSXY0eDnZW5AmrJrR4CsZANo93CnbYN7M7Q9C72euez8+YIcd9r7MAFoXWMM1fmhd06CkxBDbNF801RffHV+07qGHVLSUgdbMDQ429i/KglomWT5yEb0ZfzAa3SHLHQQ8Su27rgus4eTogXEpM5isiRX2lzQeDzpdzj80GeSJrKvnyVDblFHl/x9WdeNglRlMGW5W1uAsE4CRg8hPt/NdOd79UDaTyYddfFwFrDrtUmqhLfixD220b31JKZbLyIP2o+38OGy3Z9rfb1r+NWCFIAiwruxB4FMxCLC2X7Rem2dM0ed44lR3WwWCAGtT681wfze2R+zYvWfI4oEAa8sko80Z+415X8VAEGBdBayJ/c7w43eV/WMIAqzLcYNlgkLfmuzIcjIewLR9ggECAdbWAsuutra2/kPQ4rlAgLWND8Gzpo7dex5Eg/3aRygcBgHW9oFKn/eR2xvL6PnKeOcsnqMMQYB11S5wSuEwqsQogUUtIgiwtkdZXwGlFRSDIMC6QmV9licrX2xgYXEIsK6vGxxGguOf5Vn9HfldJ/ZZIcDaPmCTucFINYQAKwRBgBWCACsEQYAVgqBy+j+ZGa7cQ8MrwQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Therefore, ![](data:image/png;base64,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)
Find an anti-derivative (or integral) of the following functions by the method of inspection.
sin 2x
Answer:
Method: To find the anti derivative of a function by inspection
Steps: 1. In this method we look for a function whose derivative is the given function. For Example: if we need to find anti derivative of x2, we know that derivative of x3 is 3x2. Therefore, the variable terms comes out to be the same.
2. After that balance out the coefficients of variables by dividing and multiplying suitable terms. From above example if [we divide x3 by 3 we will get the answer as x2. Hence, we can say that anti derivative of x2 is x3/3.
Now, similarly,
We know that
Therefore, the anti-derivative of sin2x is
Question 2.
Find an anti-derivative (or integral) of the following functions by the method of inspection.
cos 3x
Answer:
We know that
Therefore, the anti-derivative of cos3x is .
Question 3.
Find an anti-derivative (or integral) of the following functions by the method of inspection.
e2x
Answer:
We know that
Therefore, the anti-derivative of is
.
Question 4.
Find an anti-derivative (or integral) of the following functions by the method of inspection.
(ax + b)2
Answer:
We know that
Therefore, the anti-derivative of is
.
Question 5.
Find an anti-derivative (or integral) of the following functions by the method of inspection.
sin 2x – 4 e3x
Answer:
We know that
Therefore, the anti-derivative of sin2x is …(1)
Also,
Therefore, the anti-derivative of is
…(2)
From (1) and (2), we get,
= sin 2x – 4e3x
Therefore, the anti-derivative of sin 2x – 4 e3x is .
Question 6.
Find the following integrals.
Answer:
Question 7.
Find the following integrals.
Answer:
Question 8.
Find the following integrals.
Answer:
Question 9.
Find the following integrals.
Answer:
Question 10.
Find the following integrals.
Answer:
∫xn dx
Therefore,
Question 11.
Find the following integrals.
Answer:
Separating the terms we get,
∫xn dx =
Question 12.
Find the following integrals.
Answer:
Separating the terms we get,
∫ xn dx =
Question 13.
Find the following integrals.
Answer:
Now the numerator can be factorized as,
x3 - x2 + x - 1 = x2(x - 1) + 1(x - 1)
x3 - x2 + x - 1 = (x2 + 1)(x - 1)
Now putting this in given integral we get,
Question 14.
Find the following integrals.
Answer:
Question 15.
Find the following integrals.
Answer:
Question 16.
Find the following integrals.
Answer:
Question 17.
Find the following integrals.
Answer:
Question 18.
Find the following integrals.
Answer:
Formulas Used: ∫ sec2x dx = tanx + c and ∫ secx tanx dx = sec x + c
Opening the brackets we get,
Question 19.
Find the following integrals.
Answer:
= tanx –x +C
Question 20.
Find the following integrals.
Answer:
= 2tanx – 3secx + C
Question 21.
The anti-derivative of equals
A.
B.
C.
D.
Answer:
Question 22.
If such that f(2) = 0. Then f(x) is
A. B.
C. D.
Solution ||| The correct option is (A).
Answer:
It is given that
Also, It is given that f(2) = 0
Therefore,
Exercise 7.10
Question 1.
Answer:Given: ![](data:image/png;base64,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)
Let x2 + 1 = t
⇒ 2xdx = dt
⇒ xdx = � dt
When x = 0, t = 1 and when x = 1, t = 2
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 2.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Also, let ![](data:image/png;base64,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)
when,![](data:image/png;base64,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)
so,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAA1CAYAAABofjQZAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMHSURBVHja7ZwxbtswFIZ5gFzAQNjNB7DpXkElihygsuCtyBRwyRww3gwUvkC3bM3QuUtO4BtkyA1yh7akIMuJJZsqrOp/yT/8i8Hh6X18j+TzI9VyuVTU+xSdQPgU4VOETxE+Rfj9y7t8PNVqo5T6HaWnG1u4z8iOk2DzVaavlTJPC+9HkPC9sxOt1PPWiTsyxe0FJnh8m2sbQeGvVpdn9lw9aFv4y9XqrIqo8FvpzHbDafMB8H4xqrMSKPwwO03mvrY5WCn9bJ2foEU9us1zo9dhcpb2AKf99g9Qd4iRj27zbWEutJmv68koDP7WcDO/kwIeweaQ7md69iPAFgu/3KxMN5KiHsHmkO6rJUcs/PARqDt9VJvDsU5nV9f7exBB8F9/hAQNbXPMOn/X+eYNqBD4YbPStJNGFoLNZTFnv+bwUvuTAOsIZQovCTyyzWIivzqe7Ds3Hxtjv1XFFLSIR7ZZBHxXfPzSVioNQlz/JdgMDz848fA6hVfhk2Kz2KMe9X9EJxD+25XEugHhEz7hE/7A8NMqSJhHM8Jn5BP+W4ffJUMh/Gs4dEYdbtYlfnSlISK/q4192H9q+7jmU1zzCZ/wCZ/wCZ8ifIrwKcLvW003XnPnxyhOci6fZJm50Vo9Hts/dBl7Mv/5xcgo9dSleRMCftkEWfe81RMB46pW6NVTWj8GmMfqGF3GntzGQ/WXlltEgzo2tBplJrt53exYXS9GurhROTgFaJexp1C8qdPwNkBs5dL6vq2tDHItIvxuKT/Pm+FGP2p739ZJDAk/3nYFu6SJHPn/WuOAgh42S3G9n9mfaL360uAfS/kw8Os2450/iMx8jTQBpME/lvLhIj9Mgt0LEUhlWWnwU8ra0Bs+pJc5JMFPSfmw8LebPsLvLeVDw48NJOf2AWXdlwQ/9Z9MSPDb58645veW8geHH68zh5p0rOW7SWV8fEqs4fozAvyU+kOXsb2k/ETfDR7hn8yH7y+OeHr2C+kZ07bXNpuiusvYPvdKqZVR2DWf6l90AuFT71F/APyKDt7gbNs/AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Question 3.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let x = tan θ ⇒ dx = sec2 θ d θ
When, x = 0, θ = 0 and when x = 1, θ = π /4
Let![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
By applying product rule as,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 4.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAABACAYAAAAd1In5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOxSURBVHja7ZxNbuIwGIZ9gB5gKmF2PUBjeoVgVV2PpkSsBnVVWRr1AIEdUsUF2HXXnmG6nQ03mAU34A4zOGBIQhLHjhMS+i5eqU0pX+wn/v5sILPZjEDdECYBsCDAAqzkhfn86Yr3yCch5B8hbD0Ow2tMVEthCZ9NuAhv5c8jRt5Ij38+zedXmKyWu8FQ8FtKvBVWVxdgheNrj3i/AasjK4v5YoKJ6gCsgPOfiFcdgPXs0xcWTB8wSS2HJUFR//lFxS3fF98xWS2EFaXrUY2lRDcqlYfQwYAAC7CgNsMSwd0PSshGxi+VdNR6Q4l42S2dFdY0YA9NJxuAZQlrxOhCwpHNXbm6+my4rLtIbmrgF+UGd31Bumo6bQcoG1hRx53+BawOwFLxqsmWE1wgYJ1dIuD3HiWrqtm0FlYT6XoXXGAoHm/khB+yP+qteCDudf8n+6zqf2qDpYwAlorfu1ozrTKex9WDr38i2OjtK7tAdYCI8iBUZYtcZSaHigDLQvGtH5NVlbVbfjwFpm8UNAdrf7pJ1l2MkHXcBUjjyev2HY44qLps2cAqbhrI7aTTlZWIb9vYNh6zSfYYzMZWGpZ6mg77XbHruyeHrR9FeOMqXtVhyyWsw8pKeR416cptxsEp27Zj0zw1yTdLLv9dcI1+p/SjSvGc5wJd23IJK++YXtZZy6xkzWZsxrCSboqtBwP6XrUWK4pXLm25hCX7pul7UVlj2kZezDIdmxWs+A2UObGr60zrEgsTW1n1jU6mD0Ae9DwoRQmG0TxWgdXr9f7ospwyWwllYJWx1cTKkveSd5bSFlbZsdm5QbncKf8QU/GtbPqaB0uXstvYqgtWlMazINR6gFTSkesGDcdmlA0qPzugg3cVWI/Vvb44zAKmi1e2tlzDkhNO2WiR1YZijL8my5vk/WVBtBmbceoeVfOpAcdfq0ups2AVdg4q2HIFK360IUvx9zypT7cwh6y/PLx+e12tJNOxGXUw4mcKlaHTQF7eJRbBcmWrKiwJqjhBOb0HtbMu/y5313fvQTd3PPglAdqO7WztpibPLlyKAOsSYOVlNq6BAUJHYEGOYOW1TiDAgirB2hd4+EBdB2C52PqAaoQl2/5RocZGC1llD/tsiU/qtxBW3nYzJqmlK+vYJqEbfKVCh2IWBFgQYH1hWMeNMHytQqthxeurKEPs1/9pR8gSVtTATW04oovRUljp3VTXR44hwAIswELMgmrJBveHEJENos6CXMCCAAsCLMCCWqj/0Md55sNaLqQAAAAASUVORK5CYII=)
Let x + 2 = t2 ⇒ dx = 2t dt
And x = t2 -2
when, x = 0, t = √2 and when x = 2, t = 2
so,![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 5.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let cos x = t
⇒ -sin xdx = dt
⇒ sin xdx = -dt
When x = 0, t = 1 and when x = π /2, t = 0
![](data:image/png;base64,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)
because, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 6.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAABACAYAAAAan8KAAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAcISURBVHja7V27btxGFB33dh8FGnVO76X0B8GKCZwyhiRClQUVhkEgdgAVLih1avwDquIq0jfIZVJk/yDA7hdI37C2huTsDndJzpCcIWc4pziAnrvLew4P753XJVdXVwQAAH+BIAAATABBAACYAAAAMAGO6+vz5+Eu+UoI+UZIsDhNkh0Eyh8I/C9T/i8ufkRcPDOBeBqchXHyin19EpAvZDf8en59/RzB8gPgHyZQQBKHryiZzJAN+AnwDxMgSXK6MyGTe4jAUxMA/zAB9iQIpvEZAuVvJgD+PTeBKAzfulgPxlH464SSGZ2+/wiS28NV/qEXTSbwfko/BtHla9cuiH3ubGaDfIMJdIuji/y31MvSZ71UBoYHhNWF02n8xqWLuoyC1zCBbjcGi91TDJ+5yD/00tEE0mmh/EmagT7yKSOQOn7k/C9d5h960TgmAFIBHwATGMFFJPHxSzawkz656GR2ehqciaSylDYgZCFmOOx3xZ+P/4kHbOlluamXXBPzCq3Mx6gV9wnNb2QaRgkbyRYNQXR2thx2VeoIq+Cyp0CwOI6Tl7hBPDAABb0wrUQB+atCK/OxaUX6B3F0cEQJebQ1XSpb2spnCDY/r7gvgo18p99TeocMwE3uTeol0wa5T7VynPw2Zq0o1Uq2DhJly1rJ46ZA62q8dQkQLPb36a0P02Ad6uRRDRA21cu6BBi3ViSuST8z4tmmEha8veDwxqbFI1XkyQZ6VuaGzTGq3D/Yxn1feilo5eLihVcmkK0bpzOb3b+LCezu7v6LGQR3ue/TBCil/+S//9MvE0hTJ/q/CyZAgpMvyuUAuy4a3sWX8Q/Z+ABmBVzkvg+9ZFr55TbVSjo+QB9/fvdp4o0J8MDYXAeJ9b24062KbPb3+3T/lv8trxFxeIp73HfWi3BYiqgXtkqyRisPYzxoxXkhrPYK5PU9m/I5DPZuVgNa+c/5zMCm24v/j2nCcZuAwPeS1/ileknOd2Ra+f3dp5+8MQEXamY+cMk+LxvAYlNbLHU7CKM/+GCWuByaX5O42QgLhtzkvoNeHpgZCHp54HrJ1wgsS7QyyuXU0icsBs78A7j3C/I0e6OuBvwxAXAPE4AQYALgHiaABTVemwC4hwlACDABcO+xCZTtuAOsvFmXxRmOcjQZ5AP3MAEIwXOAe5gAhAATAPcwATUhqKShQDvYbgKqZQhgJZ4hE8CYADIBQG4CGCH23lzAPUwAQoAJgHuYAFaNaYdwzuHS1i3MLnEvnAW4HOM2X5jACMF2sPHdZ2WHXsIExhdPmABQieygisnMtmzAVe5tjaezJlB1Og+gUbTpWX6Te9tE2yf37Emuq/25rfEcIjs6iOKjzalAb00ge6rZWXuzJ5euG8A1E+Dn+NPg5LOu9N3WePat8dU4ieIJyZLUavuMdvfSQ3vPEIzC8K2N9Wsf3LMjzXW/vq3xHErj6QlJwrmJ3plAmhry/oQWmgBzb1vP8DPNffrk0jyAZ3M8TWo8oOS/Ko3zjEDGY/0bELIYIrCM0K4CTJ80YZRk03F2mQC/PubQLM7TafzGOnEZ4t7Ea9seT6PZlETjvNdm3dSptGarO0zRVLffriaQNox4qjXXc/JmTEDSwbb0+vMluVYfWGmy717VGE3bbsDioaCm42lTx2JVjfOj0uvupy1nSS/s6cVZw4XDveBGdvOY6PbbxQTE8+JNm4Cp6x/qqcK5Z0duq3DfylwYHxWlgCSWVnQDtqFjca7xv1U0Lot5wQSqnuqNyNXU7beLCfAeesXPZbYccL3bcRfuW71PzaxDIZaWdgMeumNxU41nxlpdEhS+WZ/fTx+bTrXo7Pbb1gQ2/68vE9B9/UNgfRZ/c+6VY8RHsiVTjy7EcqiOxW00nplAdZmivU5puvFkuwFINeoCnQrsKZUtf6pUB6jJ+8uMybdux023MquagMlY6tx+3bRjcdf35hoXp/wKGq940vduAjq6/bbJBNRuZrMZAbod68kEVgNf627AVsay747FcUg/yE1kW+O9mYDObr86pgh7LwfQ7VjLmMBWLC3tBmxLx+JGYwIVv693bEUh6+7265oJjKnbcVPuW/FRk+K70A3Yps+odXag8E/5SGfq3HuHN3U1mYluvy6ZwJi6HTflvn1NXm4wKrEcuhuwbZ9Ruk4gz76U1wmsBjuEdI2lEnUDcia6/bpkAuLiH9c72DblvktJUMavC7G0rWPxeroymNesGJzX6V96A+q6IQH70Rf3JvYOAOpZC0wAGNwEVk99hR1uQEezpeG9zGxhAsAg3Bf2vCMj0B7bdHMRDe9UYjtIXQj4OyawiTg6OPLxIBCjMW14WlOFQ+cjxPl8LZzaoxoS3HuH0h+anCsG7MZ6zhvce20CAADABAAAgAkAAAATAABg9PgObyYY6W+NbwoAAAAASUVORK5CYII=)
we can write it as,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
let![](data:image/png;base64,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)
when![](data:image/png;base64,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)
![](data:image/png;base64,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)
because,![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc8AAACfCAYAAACfgVJoAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABojSURBVHja7Z09jxRXuoBrCCbxR8TKa9Y1mREQmT5MTrBqCuxFsqWx6SmNLHm4E8yyLdkgdYDYNhnaO2x+nawhsR3cdNcLDq+u7swvsNcQOjH8hKXn9qnu6q6uqe86p77OEzyShWGmuz7Oc973vOc91v379y0AAADIDhcBAAAAeQIAAGQQoGWtSZAnAABABoaO/cVUnK8sy375+/27AnkCAAAk8OVt571NZ7gro05PosL9Om8EyoUEAABzRboj3red4RfIEwAAIAOj0d4bjuPuFln35AICAIB5Eedt5z3bsn6dinNi92/dIfIEAADIyL5c87Sdp3uj0RvIEwAAIAPj8c7blzac/0KeAAAAafKb7/H80hUfUDAEAACQwv5ij6c1scTgEQVDAAAAVUSuXAQAAADkCQAAgDwBOvGyzQsUouD6AOh7x5AnQEuR5fDCsp57BQonsF84w/FFrhNAcVaKgFY5DjZBUDWJ5aIDVCTPntV7ujMev831MIOh61yTrd/2Hjx4XVdEVZYmX78HD/Zedx3nM8cdXivzWWXj96k8bwfk+e/oSazHKeQJgDyhrkFf2Aeb7vCGqp/pR1AaONX06zl0Nz+xhXuQt4lBnDyV3RMedgDkCWrFKdwvP1A6UC/lOVFM4+Up8U4+mQp0eglyCxB5AiBPaDhSnFoG6qXs1ky9tvsFJRgnz7Lpax54AOQJKqIj2ebNvvpt0fRiBnkaK04/qr9q29+IwfgPea5FlDzlz7piW09m11U83xqNfoc8AZAn1DOwf6ujanoeHRkvT2+CIo8RyzlBiZLn0Nnc9e/VtrD+tvaO8wON4QGQJ9QQdVrC/VqH4ALrncbL05ddnugzbc1zPHQu2pY43BmNziBPAOQJFUadjm09VV0kFJLnSuSZJo42b1FJnajsiPfznL+ZKk9vD7b4J/IEQJ5Q5b0tGLnklKc38A+Hg4v9vrhn29ZPwY3/J2VgPYvfniKe6/qsVb1LwrL/7/f7d3uqIs9NZ7hLkwQA5AlVRkJ6U7aL9U4v4trY+FGKM9w158Tnie60M0v/iu1HbY8+86Ru0+QpGzEUKfLi4QdAnlACV1hfa07Zrqx3zuU4iZOn3C4ju/KE/9wvasoasTV6wiInEhknLEnylNtf5L3jPE8A5AkVoltIUeudSfKUz9lgEF3x66WXNW2lqfx9yvFd4uQZ2Dd6Sl43xxlu5ZEoLwAA8oQS91VY4kkV651ZI88iEViXr3vU95Zp39XUtv0i7wSIFwAAeUID5Rm3v7OIPLuUslUhTyX3hxcAAHlCwfuqMRUat7+ziDy7lLLNOxlAngDIEzokz7Q9l3H9bIvIs0spW+QJgDzBUHnOxfkq6ViwuJZ8eeXZtZQt8gRAnmCuPF8lCTSpn21eeXYtZYs8AZAnGCrPCJEeh9rvxfazzSvPrqVskWd0GqMzNxdgVZ6XL5y2Tv9yeTy+wPXomjyd78pGdeGDqZPO78wjzy6mbPN+rz+K1w4s+/r3qg/+bsSFuNW3b8/32rzUcaQPAJEnaLmvn577cH39/M9bo9FvS8pzJX0bJ06vTd9cnlZv+3GaEDy5C/ega4HJ9H166/z6+r/O7dz7KO275elG1Cp5ypsr+sObC4mK7Ue8lIA8oT2Rp5r1xKBAo+Q5a0Bv/RruV5uUkhxobB3Ylsizs/IMpyPkg8BLCcgTTJNnIOI8Nu38Tj+I0tH0ofPyHI323nAcd5cXEpAnGCxPP/qcmCRPGSHnKepBnqvpiBfzY3aIPAF5gpHyDAi08eJUVcW6P695sfv7d7IW9SDPEN6a5zvOD3sPHrzOiwnIE0yUZ1soK8+5AL8Jpaonlhg8UllFbIQ8vWa/G1e+Qp6APAF5mhF5enLT2Oi+0/L093hSMATIE5An8kSeGVju8ZThOttUAHkC8mwifpDjI8du/zDp4J8jTwBAnqBUnmEBNYGsUebq4dGhdcoAYjD+Qx5RIU8AQJ7IM02eYQE1gUJt60jb8gIAIE+oRJ5dAnnyAgAgT0CeyLNd8iybiwdAnoA8WyzP2857Xs/e3o3He3tbb7qO81na9USe91eO3jkBLycgT0Ce3ZanZCDsA2892O4dbe3fPUvkCQDIE3mCYpDnMvokVQvIE5AnIM88F8F5x/phlqoVzxlcAHkC8swWbJgacCDPKcO+uOkMxxflf28L6xGN4QF5AvKM+32Dd4VtHS4aFNi9o/7g1vumSRR5Rj2IVu+IAab4jJTrgDyhank631Uhz8DRjSe6/OTt6oM8uyZPBpjiEbzrXOvZ1hGN9ZEnk7IK7+un5z5cXz//89Zo9FvdsnBs66ntuGNf1DIKlX+2WPIajc4Y9D69dX59/V/ndu59lPZ8GhN5iv7wJi9lPgLN9TlMHHmqm5ANBxf7fXHPtq2feK6SIk/9aVv5ezad4W5YAL5ULct+mSUKI/LsqDxdx9llvbMY8ji3OHkyKUGehZ6njY0fpTiZlNUvz8RxU1hTMYhnJkWeyDMUPQn3yw94IdXLUxZiMfghzxLP1YTnp5nyXESeYvsRa54GyjNwLtzaaLRzpt8ffsyLmeHmBcrV4+Q5T+keq+oEAsgTmiPPWRGRODQp6kSegahotXrMfuFvXYF47u5vnZUFQt41s3tHOzviZlCe/sN14tw9DhxHnsizM/J0hX1gYsYOeaZEVLyc8QOxsKznXuXdgwevy6q7uUhPRJ5J6VxAnsizvfJU2VsWeXZAnkN384ZtWS8Z8FOi9VAziWB6FnkiT+RZ5URWPKk6bSrviywCNDXIyHPdjZCn/6Iu04z2S1K4ETPd6eQiqySRJ/JEnt2Sp1c9L9w/m5ydQ54nIir7oZSlbNknO2lsiCtfsXUlcjA7Rp7IE3nWT570oar7YYvth9N7cipYMCiXbi5dcv5iSoP6POnyzstzNrjYR0SayBN5Is82IfdZyvZ4un/PfEnrRaAAcIXpPbpjSjQq13uzCrH78vTSkfZPyDObPMNVs8gTeSLPGq+R5n2WU3F+4h0WvdrXdmWXgkkdhvwJC/IMDPI0SkgfhGWlbbiXZVCqwYcEeSJPRfK8w31MmPhzpmfFY6B9mHWygDxhwaKXray4nb6wcr3jitj4apHCCVTi+gVGUqqj0d4btEBEnpkHh2XzjYnV237clpRg1Z/T7/JTReoW5q6wnadZJyvGyJMIKRt+UZUc2GRhlVwPkambTcf9PCxHWYg1a6YgDgfD8btcP+SZKZo6efxVo9O3/iRSLv9UncKcDdBmtciri4FM2U6DrKzX2ojetsgTkCcUvb7Csp75W9yqlmfVVbfG3ucCKXJj5En7OECeUFRgdR7PJQdp1j71T1DyHvzdWHmq+kDIE5AnlGV2PFd9Z1vKXrMcwqAHrx2hcA/yXttGynO2TimeqxgQFvIMtZ0DQJ6gQp7BpgJpAUHR/toyOvKateeMjiBFnO7mJ1KcRaL6SuQZfGiy4m3ctZ3vyqYqkCcgT9AhT09ozubnywIo+6Xd2/5r1Jjltb6zrUP/74n+rf/IK1JfoJvu8AYCrVeclcgzrrouM3bvaGv/7tmiH2R+NBnyhMaQdQKJPJsrz8U66Hxblz8YB7d6hcdAP+36uetcDXT0meStppX/3nFctoYVZDbpcT5z3OG1MuJrfMGQ13OxRIk48oRGzXZl+6+ME8csFeLIsx55zjJaJ7vv+Pc32NJu9m9Xm49E/Rm0i1ZU2y72as7PmdQpzyIpZoC6XuCs8uQelbuXQXlGRZ0nMm3z/7es1F0VpS/ZuAYI3Ifmv9et2arir13m7RRUQJ4TgLy0QJ7cp+ysJclzsfczSp6LfaFLWUatl8ZFroH79Yr70AhOtT7ylKnbqC43pG2hbbDm2e60bZI8oyJN7+/LYqFLzn/Lv393f+ts3L8H0rbKUhCeOG37f4qeikK1LTQJ1jzbL8+kpgkLsYaKgLy2l9NxzL+33pnCDRVnl5Y1Wi3PEtW2s2bktjgsMzAUladpDwIUex7q/lzIsxpmGaylLKMKg4LjXXB5KXC02Kk2jCVVpz+RZ0LkWWiG7u/zLBktFukwtDyeK/p8O5PPBjVxEpEQLdbeM7lOeQ5d55qqLRO6o50y2xNGo50zfn9bv0nBMvq0JpuDWwP5Z/J0Ie/PQlHnLGqNOWi6t/3Xpr1Lceu+0AJ5zlK1l/6utMNQTnkymz+JN2C8Y/0we7kos5fPlonyDG7Wb3i0sxYxKf/EFtsPs6ZMozJn/n5N/zoEJ9ZRdRkp2bfjJh05Np94IM82R54qBzjkqSjS6IubftTtpbEMX0c2UZ5SGPIoOpXn41Y9YHuN1qcCrez3TYMB0R/ejMtqNKlnbWDJDHmaLk9/jyjyVDxoe7Pp3pHJ18hEeUpxqv7OdUQ6VUlrdtRVfJvR8WBwsUln4SZF7YA8kWcLB23kWf99mC2nXP1WdbahjsE6eAyVbkl7qV7Z83Zv/La/Hit/v7dm7A6vNemZRpzIMxQhWS/zDHKIIdt1jUtFIc/uyXNWIGN/p6NYrq4BOy0qVIXsRXvJtv++sm5qX/pHmZ7dmsQZmT7Pc1qMSbsTkKeGAamFVYi7eWfA8t+Yvm/WJHn62y2qGrCrQlbCNqlgpwFR52K9czgcXOz3xT3btn4Kb8kJPn9+JXI03S0s7L4859tO8hQ4FB2Q/GIKxVWIx4vTFzS2kvO2BskqxAxClNJQWTCCPJstT7/KWsc9jxNn0oCkMtLxJgV0+gneC+9+eGLY2PhRinO+JStSnvNlsVexe/VznhiDPBsgT/8LFUk3FRmQdFQhBuRZSe9Ub01rKtAswpjta9s50+8PP0ae3ZanzuKwsDxD0c5t3ZHO7OfZh0VPbeqgPNci5DiJk6fcqhOVtfLXlLt8XTspTykxb7YkI6nx3ttXNsRXeV78IgOSjipEX55NEcJ8szcNIwyTp66UbXjA9n7ParRzOybSmaiMdEjdFpOnfPYGg+j3f7aefPXbLkf0nZNnoDvQsotHzgEu74A0q0Is3w0pKnquWp5+pE5aFnkuJ4bWI00p27WUAft23kinyGQu0D5vzdRneX4vXuWNPONo2v5V5Jn1xskmzF5HD/tFkYrQPAOS5irE46rluZw1qp8MIM/2ybOOKts4eeqKdKqqum1b1FlUniakbDsrzyoHJM0prcrWO6uKNpBnu+Sp8+fnlaeuezHLVoknXW83mVKEpUyeJqRskWfJAUNnFaIvzzwvwP376ioRF1WIRJ/Is+HyLJOy7bo8Q+9/7OkmKuVpQsrWSHnKiCrtpcw6YGiuQlxZ70yrQlwOAqvrvScqETN+1tk1sI9MLghqhzwvXzhtnf7l8nh8QcvPL5jCT5uwJe3vzCvPspFOWfk2XJ4nj3mM3hqkRJ6mpGy95+7ybz63fnP5f1Uft9bYwS5LAVFWeVaQsj1e/J6UKsTgg55UiZh3okHq1vDIs4A8A2JMG6yVyLPsfei4PBdFQPP/Pg4P9nHFQkXkaUrK1sjIM8uLlnVA0imXqPVOv09v3OeX22XiKhGLFH3onBwgz07LMxztZI508spThfi6LM+Y675yTzLei0zyNCVlizxLDEg6qxB9ecY8yMdxm8eTKxHzp96oukWeZZ+BOIGqkqeKSMcweZ6IPlXJ06SULfIsMSBpLqRYyytPHYO8CQ3yyzSwRp65BLoWuuZK5KniHpgkzyiBJrVIXCwF9bYfp63tec+KcA9M2S+LPJspz2NV8iwTIXddnrNrYz2dDR75G1gjz2LRZ9qZkcFopwrp+e+ISS36AvfkVNR65/xAjV/DtRNJEehAdmoyqEYCeUYOSOkVjGUGlbRIJ25/ZxF5lvmculPTdSObafjfzWs9mHNrzp/Eaw8t+/r3bZRn1i1M40/Pfbi+fv7Z9Oe/pWCwXkuKdGKinbW0SEfBNXzr/Pr6z+c+HX9okDxfJRV0tRH/mMSqvg/yLBp5Fq9CXEt7aOO6ChWRZ5noqOvyPDnTzrftqAkFVUXkeXd/62zPto4Wz6HdO+oPbr2vK/IMR59x8pxHOy8iop3YXssqIh3T0rYRAu2EPGXkW2WxklHynG9VmaStp2iUZ+qeq6R+tnnlWVZ+RsmzgITaKM8YQXnPYlRzdJVFY2nbV+rCVHkGBNp6ee7Px3a7v39H9b5L5Kl4QFJYhXgcjjpVybPsZ2yaPOX3yXtot3cweYbP76d8cr08LZOnv8ZrO+7YfybGw8G783XfyOO8NMlzgjxB4b37JjQxm1hioL3RP/KsSZ5BUYYqEWP72eaVp4rN402Rp/zuRZr8S+RJHGnpPddxdvPey7bJM26CsCycsl+G77Xq7UpNEyfy7AaeyAqc/oI878f3dG24PE+ksZJOUckjTxXia4o8VUXQcdWUcpJRZO2srWueUciGH1HtG03Y64s8kaex8lzdchBifk5fnmbpmeSptgrxOFBMcRw3OfDlmeXswVkl4vbDkgOzrEJ8VmcVoqrm+3GN7v3oXF7P0WjnTL8//Ng0efrXOOq7IE+oM/jJGgwhT303ZpJEXZFn4POtNHCP/F05qhAlKioRmxB5qjrdxW+aH7wm3vaUlWtqv8jzXbsiz9nzJQ6jfgby7L6QqiTqc8qWfvPCpUka84KgNeTZUGqQ58pid5MGlTrlmRQRRd2PtDVRLzWp8Ji1rshT9kSOm2jlec6bOFjnOQmkg/LMJKSK0VIJizwNlWdQoE2bkdcpz3nE/TJLBJ3lqLlZ2vtkUYzJ8kwrKsspz6YN1JMsBUqkbdsP8qwwjdE0efqDD/JcHdizyC5w1Nyd1I40UxmraqnXdnlmqWAmbQvI03B5LlKAfh/Tkn1rTRlU6pRnXAVoeNA7uccrWmi+PFUJr83y9NLcwv1zpugfeULT5Xnbec/rxdu78Xhvb+tN13E+032mqDHyDPYxTVv7Qp71y3M52Ume6CwklvGQc1k0pGrds63ylJ9bVmKH1wZl2z4hnP8MXhvkCW1hIOwDb53X7h1t7d89S+SpY8BJ6WOKPOuXZx7R5ZZnBiF3VZ5Dd/OGF32HKrx9wtcQeQIgz8wDjg55trUKsaw8i36WRYpVoTyX0ayaoqG2yVOKM7mw5uRWHeRpLioaziDPDkaeSYUSmuTZuCpE3fIMNuJP378VEfEgT+WRZ6EsDfI0DtnzWNjWYfjkHSRquDzT+piStlUXeZYatJGncfKsI9pBnpHvXuTJOxcH964jUEPlmaWPKfJsgDxzrE/ml6e5a55NlqeMdrKeM4o8db7z85N35tWqgZN3JlEn7yBPQ87zzNLHFHnWL0+qbc2SZ95zRnU853EHB5gWdW46w92wEIIn73CdDJPnbM9gtj6myLN+eS7vWXqKNbh/czTaeyMuLb+QJ/s8s/98RQcgZI52Mp4zqvgaygMQfj63c+8jpBDPrBe0eEbkaWDkqXJAQp7VZAqyrk+6sz1eE8sWh4Ph+N0kydJhqFnyLHLOqBZ51nh6UDvGgum9yHCikzHy9N5/5Ik8GyjPPL1tMz/snette/nCaev0L5fH4wva7kGNz/miy5TGaIc1z6zvojgk6lzyJ/HagWVf/151s3vkqZi6qhDbcqpK5oG4c6eqdFeequ8/8iyOzOyomsQiT+RZ2aAi26bVVYXYiPM8FVTHqjpUG3nWEO1oSkkjz2zI8zb9QkuuB/JsjTwXxTA1ViHWOaj4ay1lpeeJznaeqrxfyFMvSeeMIs/qJq9yPRpxIk918qyqCnEaLSVWIWqclc8LKZ7VXUhRdgDXNQlAnvpIO2cUeVbz3smTdxAn8mydPBOrEBV2ymm6PAMv8rjIv5Un6uiIYIyQp+Zq3qRop8r3XVjiCcUwq/dgfvLOqWCthZy8X7rk/EX3cV9dludAWF8npcG7L8+mVCFqHNSakLYNX3PHHV7LJU7Xuabr8yNPfdFO1e878gy+M97JOy8STt65QzRaTJ77jv3FdBbyKukaIk+NVFmF2CR5NnF23nV5VvkM5DlnVLWwvXeZaEqK8xPvTMyEk3foMFQu8kwrwEKemmfnSeeRIk/kqRLZWUZ34U7ec0ZV4jXjYPM/IM/uy7PKKkTkiTx1f895tJPrnNG2TQ4AeRoiz/QByZQqROSZ+PI8lC9P1+XZ5bTmbL3TPuQZB+RZlTwNqUKs+jsiz+bJc7HXVvO+4tqyB3L/L+udgDy7Kc8yWzWQJ/JUIpkOrguSsoWq5bm/kOexmfI0qgqxw83vkWf26FM2EuhSpeXs+b76LVEnVCVPKU6/mtnu70duV+m8PCVyr6UJVYi8KMhzMYnryNqnPxkg6oSi/HEqzzX7+j/oMFRgQKqgCvFGnVWIVUwOkGfZZ7Xa1Lo8XaMLTcK9wrt5NodnGQqNz5oa5hshzy6nNWeDsn1EFSLyDEdsbT+eysvmCPeA5QhQKc/wslrR4yONkKeOY66aghdVKzz7Enl2Q55BgW66wxtti9wQJ+iQp3wnrtjWk8gMoRg8CvcIThKsEfJcSKaD64KkbJFnuoica47j7rZBRJ7wHeezvL2RAbJGnonRpGX9O3kJbrluaow8u9hIgCrbFspzNDqjImUEAJHyO/Fu7bPmWU6efvTZFdn4kwGizvbIU1jWszoKygBMILi9JEzcdhOD5Zk/FSb7zVbVNk8nfhUiL03Ga9WBew4A1UewyDMQsVXVsF0Xs2KK7Yeka5EnAKhltaio93xrNPod8gwJVFYhIk7kCQCwGC+czV1/GWVbWH9be+fKD1t7e28izxURta4KcZcqROQJANXw5W3nPdsSh1HRp9HyBOQJAJDkGGGJf8oqeeQJyBMAIItjhs7FTWe428HG8MgTkCcA6EE27Ig7YAF5AvIEAAgh943KXRkdPQybri0QeqAjngPkCQB5xTnvSnRKesZxhlsd621L1xZYMpx1GJlEdxhBngCQjtyestqpyH4Rdbg8FwsAACAnXAQAAADkCQAAoJf/B8n0pYa1UVP1AAAAAElFTkSuQmCC)
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)
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s3PvALXdPfIa1VBLWOQ011A8FgTNOHXfm+dT4HAzb4GaLLog1r8IC0dNNP7v1uPIF6vwS1jkNtkfDvH0HfZuXvbOp/jM2m4+yayzNAWvrpJ4wPGnDNUxLUOg611U1cNmZTToesy8Y3FDgQ+QHTrlNHCGoBQG3hsY0u8wkUvLSAyjTIurr2+DSP0xf0Mx9vl6CmgtppOOdymAcZGVm9nl3ZCGqKt4X8AAp2TF4QGVk7THdwDEGNjIwsbI+ORCAjIwvJ/g9+5eNPmtxcfQAAAABJRU5ErkJggg==)
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![](data:image/png;base64,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)
Question 7.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let x + 1 = t
⇒ dx = dt
When x = -1, t = 0 and when x = 1, t = 2
![](data:image/png;base64,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)
because,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 8.Evaluate the integrals using substitution.
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let 2x = t ⇒ 2 dx = dt
When x = 1, t = 2 and when x = 2, t = 4
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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
now, let 1/t = f(t)
then, f' (t) = -1/t2
![](data:image/png;base64,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)
because,![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 9.The value of the integral
is
A. 6
B. 0
C. 3
D. 4
Answer:Given: ![](data:image/png;base64,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)
let ![](data:image/png;base64,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)
Now, let x = sin θ ⇒ dx = cos θ d θ
when,
and when x = 1, θ = π/2
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)
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)
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)
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)
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V/ZNCz5GKdHnCbXWvGFwELNTpqSfe2V4aEXH8OKw/oSxXnFFWDyaDP3kdje01rbatP3YaFj9uAOwoVU8Cw8oDe+Yc7eFQEfZm2ThX0ibUmT+q6u7Qgp82BCcWhyGijy9cXd0u6wRPACugL++nLtnWKI7NEK0PBh5VpSSFNFGbVyUOQ8wx9weQc3lLk7TsXbf0x8OkcOSwYAA/oW5a8GXkzykHR1inOyMtfhP6NeF4+FqH1GD7w/XushRgC6OdceFk8WratM8+1h0AAfXet/b5q7n1eW6fYyw6BAPoeuYP+0tI/+RNuSr3H9b+Bqw4B9D2W0PPu8GfZqUOC9Cw7AA8B9BAIBNBDIBBAD4FAAD0EAumR/B+AEb0SF3latgAAAABJRU5ErkJggg==)
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)
![](data:image/png;base64,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)
Now, let cot θ = t ⇒ - cosec2 θ d θ
when,![](data:image/png;base64,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)
![](data:image/png;base64,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)
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= 6
Correct option is: (A)
Question 10.If
then f'(x) is
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAARCAYAAABuDKSkAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJtSURBVFjD7VaxTuNAEN3roT8Qkw56WLuki8yi40oknJUrpBRRtBICyUWEnHQp7j4AKuhyX3AFlNfwCSfBFyTfENjxZu21Wa+J00EirRRvXmbfm3k7YzIajchXW19O8DvR8vPNXLZ9Z7CK/zfBrRKnNrb+kiTRFiXkWQJf9YKgf1nchykTyb4t0KB3uucB/JW4Oa4WPbrtxvGmiYnj7iZn/gUQMlU4mALt/LbhjmjrNsUAfYpEdEgpT0zMKnwLD+Nxd4NTcpf+YYc9dsfjDdwfcnpCCH0ORbJrF9w+kEJmPhdnKSHB9vHZjIGx2Q55JMAe9J7g/lkqzMDh6lByjwIKnGjnvnxuU77EFogBecBANEx+YtYZwJ+qCmdiSqQ4hV94cJQkW/jcD+BSZn5WjqP2VZWMCr7g2YWqlirdlG9lI8stQl88DyaUD0+qAuiqujBZYkoVtbkiw8oEBWH/R10fWZavs3srixRt48I5E7OonlW0/k0S1q7IbI/nA/z3w35YJ/6jfGtFA8A/03quw1wYl+i8srlo5YBwl3mtm0y85U434Vttb7QcHE/EUHxX9wVm7d7gwGXvlHQcbzvtbbnTWUIqRKF4CuTJ5aZl+FpFx3G07YE30VmvE5ULUtXA8aNnJGZfEzUa1pWt82scxgtocG2OMVffWJbvO9Fp55MCysQk4St9X057g70Ki8/NmYnZNseT2WX1HdXnEcrvyknU8xtxKmH5JFiVLymOmXTmpS8X+l4sKjTPl33gY4YXNlQvJx67Kc9JNVdxlOWxfMYvzHueimb8XIj2YRZPvqDYZm5Tvut377XotejPtd4AubyWkJR0ZzEAAAAASUVORK5CYII=)
D. ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Applying product rule,
⇒ ![](data:image/png;base64,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)
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PtFlEAyFAdEwpgMX/9ke2PLnXCPE2zktxe2njQni6hWh2kynW8zhvqhyWwlTin/RA+zm194KgjSEhISFz25EkJJCQkJARpEhISEhKCNAkJCcliyf8BHpKygfSSVhkAAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAABACAYAAADPqEHkAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAfjSURBVHja7Z09c9RGGMeVFFSQisYMex0Zhs63vjIMhUcWb6Vjzho3QFx4PJoAnrnCQwSdC6DHaexU8AWSmZgvAJ8gzJgylf0V4sutpNXt7a2k1Z3eVvcv/gX45lbaZ3+7z/Pss3vW69evLQiCzBc6AYIAMwRBgBmCIMAMQRBghiDADEFag8myvpOFfgHMkGE6ONi+7BDrZATwkNr2S2JZZ8TefYG+AcyQgfL9rSVq0b/X99e7tu39jD4BzJDBeuXSB5ZFv20NBtfQH4AZMnl17ju3Ox3rH7jYgBkyWPs7q11CN9+G8TP5uLqz30W/AGbIMMUJMOoe+Z6zzBJgFnFOtg8OLqN/ADMEQYAZggAzBBU7wFBAApihYgCqE6Tdfq8/ip3PWSEJsXf3YBuDYFYNIszK1fQv72NlJZbjPa/6WcP9Zusi0tCyyLnj+cuwowEwh9U/1jfBgILIGQw5vzyHPFf3r3Uh7us2oRJrk5K3zOae03vCJpTOivMemW2DYO5a3ZMt319Cx1bsztrkhVykUWclVjgWyBdM4IBZ/f2es+y43r1Wr7yuc28WAFQw11mJFe4zk6+AGTAr4y9qe08XwSAuJW+o++rBPDDXXYkVxcvDvO8BTeZGWgdzMDCJ83FR4i0G4F1CPuQBUIS5CZVYujCzAevZ9GlbJ2qWL+j1d/u6YLLP7fbt+11ifZnFo2o0zMHAvG59WrQZPoDhuvNJF0CVm13784fbUYnPNBhsX2FeA6Hum7ZO1PHEymw5GFzJhj9OcA6Ng5mtummzst+nD/MMalOU+d7RzgDt+w9NhJk9T9qAZCsQy3a36WQV84KSbOpS68iim8c6K3TaRJjWRq0whwa1jpMMyldl1glti4fS3puLfUZ3ImsqzEm2C/7eokMYWmN5tELrFM4kwawzbgqE+c6tq9bVf+/4/i2t2MAme7wySBXwR/HeeZkutk5hi24BjPx31ed03nvSqHqFFls3Lx1furnVmEkvDebY6yjJrjXZ9EWWTdO2CsV2VDAr2vhe+SxVw8wTPOPKoKjwgbpH0wOivKqh/Z31H1cI+Yu336Frh3Jcw+I61+k9C5JIUfEL6W6+U31ujXYOg88Q+rm/079NqevP8t7yZKaz4jYWZoVnEf5tNKhL2PWIbPqnYNPfm2JTnoyUV2f2zJRYn3k7rkt/EWHO00bqbJWnPDPPyqyTJAnczNKMvtploPRc75EIjjj4ggQNc/MFd9Bze4+CjpQSGqL7wzqfx0izJocmnkkjzDAF5jh0KiEPEtn0TLLpmdhW3P6kTTeqsKnq3QeDrWsjL+WUOK7P/s/3+jcisIfqIqD0NlSZtEypan2LhDl+8RJgTorF2f7uqL1T3l6SZyAnd1TJquD/qPvbXDDz8liNgd80mMOJeBrm+J0KzoMUaNM92aZ84SrCpvICpcqLJCUPc8FcZcycmbXTGMizehI6sXjaCiKv4uODDeTc7u/ez8pY5oZZY0IrAuZ5PTMtmDO8jbbbNOyXcDJJCqOSvstcmBVur6xZPQmdgoa0yUQFWex+swFMyNe0QgFdw4+9k+y8QREw5+pPrUGbH+ZZn6Ekm24UbVMR5rzQ5oK5STGzDsyzSmh3bxbDJ4UALN5xVjrv4wHQ3fzDJJgrcbNz5AGaatPkTHWDYG5SzFwmzPF3p5woSgNJFfdNunzjJIZqpVhomEuKmeNkV5ZNI9dZLpWtyqZizByf95b6on1udo54caZkSXR4n3Uky2Byb4NVnHFjRZPbcHorIcyE88+x77Op/VLMhKbFcPlhriZmriybzcsbC5ykJ2w6Wj1FmwaHdCZtesH3g+VMeJk2lWP2aIyfyhMQ/y7ZC+Dwp3kftcEsulzh3p/zZGoLoaStKeEWjOFY5FzcshAGyAWPl+LtKmGPL67uoZtv+SCK9lJPVc8eryKK925LNjttnzkEanp1rNWm0cGUuW06AjDJptyeIvCxNzzqp/Xt7R/YnnPk1of7ycKzK9p4LLdRG8zjrYNoU97zbyTFF2UMuKDOlW/WswKDFee9/Azh/mL0jFGBQc9xf51abRz3seet/iRu/svfpfves7ikBlaAnZZRfjqHTZ+VbdOoAmxqMuA3sfDnDZOp088ktPFfUhu1wpw9IBb33qgiKsDqun8tqzY7WJE0TxK1QdzTLLt+vrEwV1Gb3WTNW5vN40A2y1d9OUEWzOEqo3+SyGTFLnoFB0sKhLnY88zjQ/btOjWlqyDM0BwA8qkpfsNIUJzA3NrO2mEdlxOk2S7vWV9TV+TgqCe5+6GK/m8szEKc8W3RLgnMeymDDHPQbwJIbGKo0sPRgTl2ud3eRptvGqny3RoNM5+9F/KmkRxumQxz1r+bFO9DCwJzPDCYm7JAyRJ25C1P4g8wQ0bAzAeHfJa0rQouuJvzds7aYS75AgLIYJg50Lg3u7kxs1i3LybgAJnJMA8G1/BbU+UDI4pdRSRns/l1veFVxeVnU1nWNihpZLd2+NtLax16iF83MRjmsNYUvzVV2sqt+VtTQtx6VkXfC7bnpZQXiJcNhhla9ImGlyWSs0X59RHADEEQYIYgCDBDVQ4qJD0BM2S+6jzgAZjRCVBBqvuAB2BGJ0AFqe4DHoAZnQAVpLrLSAEzOgECzIAZggAzYIYQM0OAGWqq6jjgAQFmqCRVecADAswQBJghCALMEAQBZgiCdPQ/iCRKZZ3YzP8AAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALsAAAAoCAYAAACmYouHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAYgSURBVHja7Zwxb9s4FMeZDJnaTh2uvdBbD0G3mvF4RYdAYZp29BWy4BvawkMQCNfkAA1Bo2TL0N7edEk69b7ADU1vv36CQ9BmvCXOV2hyIiXKtEyJkmLZkvyGhwCuapGPPz7+3yNptL+/j8DAZsHACWAAOxgYwA4GBrCDgQHsYGDFQozQnGfz8l+AHax2dnDQu0ExOvEAvySG8Roj1MfU3ioc9mBWKQ0GBuyaUVtlPIK7bvcOQeRTe6fdNAz7l8JljP9CdOY14Puo4XNquw+m5ayqDCrAPWo2xVtqptAlNja3xXN7FnmCEDnrOs7dicDeRM2TruveKQs8rk0fUOvVWhUG9ZVF11Y2dpoAfTrbNPC2DLtr0oeNBvrX++z3wjV72WB3TfK0Re0XVRpAi+A3xHSfAszZYN/ZWGli0nnr63f8JwsaMwM77zxe+9g7OLhRtWRrDeOPcYNVRi09bdh9n6FPiFhHbCX3EtRzhOmJauxrBzuf3YvoM7H2nlQxYnHtuUg/9xznZpnb2SH4rZeLXUwrF4vKmFQTtGqw6zQtky8clpJGdW37/UT/W9nlDJNc4y48ZMlXag87kyfEsF/qojpb0soIiK79A5DQUZkn7DR9UxLYH92/jW7/98h17xcVETtN9CGpg4FmuyijhEnT/iEp40mEvNo90NNzVQGd+4ag4yzwdpcWjheWuse1g505w5vJrKR0FZSWlFvCbLan0ZGRjYq5lM8pn41uUcc9k6b90UmbNXJdJ+rl6VP0c/FZxLQ+zuKbWsMuKhRsE4E5JPj7XSVVWHTgGwsJUmpno/3TMsZ/iY2JBll9r0oGHad306Rki2f3/sZYHzc7f8jPsmdWSeOQ/zsmX8wN8yEhlpu3/VHYEekcTxr2NH1iPvSeeY8RPhWBJfQXRqcs37At+phg9A/f/In47Tq+GQvsmm3ZeV2EK1rG+Es7n/3biXo9AXZekkSo37LsZxJU/ag+ZgPHv0sqYdlW6xkfDKlSIi+97P1ca8cAqmu/Ikk9y6vbrwO7rk/MZ17bvvpwDlZR/lwArRdADqllP+Z+83dAr5KkZRbfjAX2hG3ZEVMdtJk27DpA4pJXv6pAvsoTJE4O+Z/7bRDvY1Fs6IwGsXbHBrtmlRo37Gn7NAgswz4S/pHBTiPJJg77JGVMnlVEC7tY+mNgT5u8hgOp+B75Hfae/YN/2g5fGObmuk5rZhnQOJjS+pJpYEn/zqfJT8L3puyTLxnTw54kyWoNe55V5Lqwi/+vgz1phYhG3EDacO2PMD5tmZtmHBxFwR7jy8tQ/0qWpkqVtk+Vhr3qmj0t7Czi5YVdlRe4tnmPLjfeBYBcoWbng8o/RcFeRDUmTZ8qDXttNHuMzg2drjgGKpfRkkAL3xHofhkABgjB6Evc6pEP9slq9ix9AhkzQdijkUYHiHSjhUeqdq93S6xU7IiBPECighA9LiqqOaS7t86+zyDGa7mklpQX6NpfhmpMlj4VCfvM1tkjTuszUFlp0KL0RRQE1QAMObVL1qWabmC4Hz0lJ1/1CjTrfK/XvsU/C6K6eAYT6w2DQySG3mT7lrCyJLZ/dAWZbJ09pk/b0T45TvducFHnSlRuxC6oHCT4nQJ2Von5eZH+HXe4TeGb57pJXmvYB2XCYLPDdu+pBlmnc3md2F+auSRrLNN3qu/ya8zB+4LbVi1q/SYGgYNBree2vfJz+H0x7Urb/izlOl3SGncPUwu7pk/hMdohWWvtBsFhSOqOSOOYo7dZfDMzsKeM/hdVvwDhR8PpHZ+tgqlg1913rhXsofzIufyXxbgcSIiCYPvo16WFIxn2IJ86Z7J0Zm4qhRdvS3I9MNeErfDlk0mZnJeI63hsJeT5TmP1UJUf1A52Ed2rKmW4hIGongl2HuCk1Zyd01EFi9rBHmp3dge15FfbosYqEewUIGj1bLBHq09x1ahawh5WXYi1W6XfjbEN8pLV8AFmgD0X8FX63RiI6BWDve04P8LP34GNc8VT8RSc7PQ1O9ss9DS7WMVZNatwzR4c6i/Vz9+BVduSzmyJjTP593aSfjMIHApWCxvs7MYHVnAU2OxIInACGMAOBlYz+x9gzzHvzbCKKwAAAABJRU5ErkJggg==)
= -x cos x + sin x – 0
⇒ f(x) = -x cos x + sinx
![](data:image/png;base64,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)
⇒ f'(x) = -[{x(-sinx )} + cosx ] + cosx
= x sin x – cos x + cos x
= x sin x
Correct answer is B.
Answer:
Given:
Let x2 + 1 = t
⇒ 2xdx = dt
⇒ xdx = � dt
When x = 0, t = 1 and when x = 1, t = 2
Question 2.
Evaluate the integrals using substitution.
Answer:
Given:
Let
Also, let
when,
so,
Question 3.
Evaluate the integrals using substitution.
Answer:
Given:
Let x = tan θ ⇒ dx = sec2 θ d θ
When, x = 0, θ = 0 and when x = 1, θ = π /4
Let
By applying product rule as,
Question 4.
Evaluate the integrals using substitution.
Answer:
Given:
Let x + 2 = t2 ⇒ dx = 2t dt
And x = t2 -2
when, x = 0, t = √2 and when x = 2, t = 2
so,
Question 5.
Evaluate the integrals using substitution.
Answer:
Given:
Let cos x = t
⇒ -sin xdx = dt
⇒ sin xdx = -dt
When x = 0, t = 1 and when x = π /2, t = 0
because,
Question 6.
Evaluate the integrals using substitution.
Answer:
Given:
we can write it as,
let
when
because,
Question 7.
Evaluate the integrals using substitution.
Answer:
Given:
Let x + 1 = t
⇒ dx = dt
When x = -1, t = 0 and when x = 1, t = 2
because,
Question 8.
Evaluate the integrals using substitution.
Answer:
Given:
Let 2x = t ⇒ 2 dx = dt
When x = 1, t = 2 and when x = 2, t = 4
now, let 1/t = f(t)
then, f' (t) = -1/t2
because,
Question 9.
The value of the integral is
A. 6
B. 0
C. 3
D. 4
Answer:
Given:
let
Now, let x = sin θ ⇒ dx = cos θ d θ
when, and when x = 1, θ = π/2
Now, let cot θ = t ⇒ - cosec2 θ d θ
when,
= 6
Correct option is: (A)
Question 10.
If then f'(x) is
A.
B.
C.
D.
Answer:
Given:
Applying product rule,
⇒
= -x cos x + sin x – 0
⇒ f(x) = -x cos x + sinx
⇒ f'(x) = -[{x(-sinx )} + cosx ] + cosx
= x sin x – cos x + cos x
= x sin x
Correct answer is B.
Exercise 7.11
Question 1.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
as,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 2.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
let,![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAABPCAYAAAD1AEDmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAi1SURBVHja7Z29ctRIEMd1OZfDlccZD4C1Dn0RtegoYgpb5QiK4IpSFUXg4IpakznhBYiODALiCyC9xG/gquMJzu8Abu2ONDs7kkZf3pX0C/51nLz+0Gj6p+6enp7g3bt3AUII1RWDgBACHggh4IEQAh4IIeCBEELAAyE0SnichMHHIAh+rGkv+vby4uIODw4h4OHUxcXLO0lyfneRRA+i48Xvr+bqTRifP+GBIQQ8vHQeh08EGsADIeBRS8k8fBEliwcSwgAPhICHlxaL03sHgbo04ZHM509PF4t7PDiEgEehJFTRCdL035IwDU8+8tAQAh4IIeCBEAIeCCEEPBBCk4LHRmWpJR4cQsADtYDotsSzQcBjAPBgHBDwQI28DsYCAY+aks1x0V7wbWlE4fepVZYCDwQ8Gkrva5F/p9vzJ7YdH3gg4NGBZGu+Cg4up+R9AA4EPLqAR7pJ7uDrVODRxOs4CdX7IFDX2ltDCHisPI9wnrwgZAEeCHjUUhxFz8l3IAQ8ammKXcQABwIeHYBDzV+9SUOXxem9+Tx5iteBEPCoiOHt7unTiOdteEi9y6Nw/0N6XR1cnianR2EYL8zvWSTH9+UzKlBXeozk++Lo8LVSwVXahS2OHh+o4FJ+jgpP3ksYKEAOg+C7Oc4C6/Xr5FHQgHMeUw5ZBKLa+xIgpFA1OqqlyWSHoZvw3Q8ffYji5LH25uSaDgWzn2kdbSHNp6U47zhZ3Oe5oEHDI4kPn6kguNZvxynAQ3sAZs4nvWZ5Hnk17rqXYINCw0bG0RxDs5pXPpv+v1Kf8TjQ4OGxfAsOP4Sp2pnqClkyKKw8h/Iwzx8edj/YPFQJv89m6hPd6tEo4CE1DGIUUrIuE1/c8KEt3fpsbXddF48r+x6lrg7j5Fkf8FiDNCfzoTHAwzyCYUyhiQsURR6JTohm3+cw/K7gsbe39+/YQ0M0FXikkz1fRRgbQHzgYUJEr5jYYUXrsEWuq+hzcp7cdeVP0LCVHt1aEfque7zR46rnP5h8x9hicNv7cMFEch7zcP7WDCG08XcJD/HuZmr2Se8dyj4zwVYIY1R6bGuD7R2SLiizO+Cxw3kQnTDVdRk5ENaN2qzLMMdJL8GaIYid18h+hxWmZAdt3Xxuasu1uiZmDKGb9iib5LBkbvyh1KciD6TyB2STyNBtGrKe7GOMwasSqKlhR/HzJHl4pMMVKRQzjTn3EoxCryhe5I2U8uKvjWd5A4ZoFnwxP+N+5tMJYcx7H/qc0y+GIntNkuMH83n4VgoJi+41tT950Zyd/drI88gKkdTt99TQD3OsCTwaC++utzv0OZcZvsPrSL+m1JWAo+xeV17tfy4A+cFDu8VbWMIb+zm1wAN49Ol1VNmNz73GYfC3y/sAHjsCEIwWeHSe63Ak1pvc6/Iz6vrhn38dDBMeFC6h3gwtXwJPQ/PT8IV7k+BwNg8u7ab67/KBxwpE/9ufAR5o2uBYzW1JMqc7jQ2QbGxIHNDmweXfW73UXgcetvffOTxcqzNF8nELXQ8NoU6NzJpbriT9kDYP5n9rR/BYJU3tvMfOex7AA/WdF7ANp8ighrJ5sI691oKHwOjs7DfggSavIsMpM6ghbB7Man86gsfSywq+2knTUcBjVw+ERrt9GHdTeOz65sHBwoOcBxqa52EnAgvDloFsHsTzsGEEPFBfuQErseiCypA2DxbdVyt46ARs7ZzHDpSn9wWPIbvdfWus4UrZ/NronXJzXXsadTcP6oO4XInVJl9zrQKVrwz5w0NAefPfX0oTpnVXW7a9Ma7vClOqO6vhMfb71B3qdLPoZfc2dX0Yxa8FKGYz6TqbB7cFjzzcLw6rstoNj1RCBo8mdR7bVJ/wAByMz1jlW2FaI4fSrMIUeAAPNLB8jufeFh+12tuyTRVlxDEO4IGK5bur1kdZFW6TXbXAg3wHGp703htzhaQRhFTwtXE/j11wv7ouyGliGDqRNZVjLzHAcXgfbUKX1p3EgAfwQAPOfWyrh+nWb95x5CLGATxQPYDYR5T6SJawB909va+tzxgH+Y6pAWQS57Ysw4Pghxw5INV9j/bDD11Wto7FMGQZu4/NWYADec2TXQ1T6m6ga2Mc4t1kJclSgp+cHtluni5bNk+vk++Lo8PX0oFa3Dt93ocGX1ru3GMbu9uEh9z/TKl/9D0UnRecjUl2HIS6Ns+d8R3vsrmw6y0AgccWlZcLq+smJ13VNQ5Zx95oOWduitJ7e6zJapYtizFpt9A+qa2vNna3BQ+dtNaHbBft2sxqC4zr2UHdxrWq8bZhNLQWgMBj5DG9/XZbO5JRrllvwnyzkf+Rjn23sesDHna+o6jYaBlarm+8KiqJNvdf+I63e+x3vwUg8Bg4GMpi9kLjkElfkVBqfZh0x23smsCj7vj4ljm7vI6N8TB2qPqMd59jh4CHc+KXGYjreuZapzG4utLuedfwyN3t+i0G6jRZKjKsJuPje1ZwWc8Xu7+E73h3NXZogvDIG67UT4oVGUiR0Wz0cXAYflfw6KqNXdOwpQwgRfCo+j1l8HD1l/AZ7z7HDo0YHmZcm07MfXd23ze3UQUPEyJ6xcR+27YOWzpuY9cm5+GCh+uab8esopzQGlgcgCgb7z7HDo0YHukbz5hsYrh141zbGFzGIZN+Hs7fmmAqivPbwKOPNnZtE6a+46OTlXI/5jjJMzLvu6gxjTmedca7z7FDI4aHbRhtXPQyr0Mbh1mLsDSC9Ylp1haYk1wvI5p/mx2bZ7+jZhu7bcCjNNdgdc4qXKq9+brOY9irNb7jvfF8Oh47BDxqGUghPKL4eZI8PDLPKzUnZP6mM4qVoniRvZGNAqaNxObN5I5mwZcmbez6hofP+JhjkI3Pqq7FZbTLuoxlhbC+L93Oz3e8N7297scOAY/WCULE+CByHhgH8EDAw1ptadGToCqeR4wPGhk81nMNxLQIAQ+EEPBACAEPhBACHgih/vUTopb6G5Xf5mcAAAAASUVORK5CYII=)
as,![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 3.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAA1CAYAAAANk8ZmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHkSURBVGje7Zo/bsIwFMbfAbgAUt7YA4DhCsiqOEAbi5UJRUIcwLBl4RDd2hN0Ye3CDTpwA+7QxgFTExIHKhB//A2fFJjin9+f79mh2WxGkF+AAEiABEiABEiABEgQIAFSndJ02IgFz4noxyfujSbBQlKyO5YqeTbPox5PhJr2zfNUiT6RWA20biLdHMWC3iwkAwyQStJORrQAJI+0HjTbxEuZ6JaNKorkYpimDUDaalODeA1INalm02v3G5CKUZS1+i0UF9prop9MKgqhdLCQcgBEq6IXytPN8Um2oF8V0qab7Bu4she7XKr91aMcXiJbbaZlDk/E87K0u86uZi+W7yq3l77WG/RYsgv9moL5EJCOsfTBQzJKVPeFWX6csti7hWTqBBOt66bkSmX1xbRRRFJN6jHxt9s5zgGprBuecsxxc4XbmjWWSvsWH2wkFXfe532ChmRTrivV+FYi6b819mI1KYqir4euSefobsf6JfgkjCUlNYg7n6cs9FoD7t3NbvcmQAAkQDqj+cWVkrfLbmwPIFV6NXtsC0gVMh9PmEHcvWICpKK/E/G8eA8HSE6adbjzvnc5CUiHaWaHcECqaPfuSQEglbX7rA65/wHSEYP1ocphBW0mEUmABEiAhKMSQApXv7yCd2xtLh4/AAAAAElFTkSuQmCC)
Question 4.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 5.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
As we can see that (x+2) ≤ 0 on [-5, -2] and (x+2) ≥ 0 on [-2,5]
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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8dzj1M7/KJ4vSMAV5kx+1QtICaBLy0O4CygJcmbrGMUnh2Yf3CqGTjuEQ7gDKAF5QmSL2jK7sDmQR4We+jrp7J+lxSekYIeKr3JP5s/GQOHYAXW3qD952LyRqWBbyq+Kmv+DxkFvm+YAcwLeCx/7clSM4QAR7nc3I82p9J0qj5OrTVErZMizwbmoyQEHNIEyjGz3Cb93tJgKfjfuj/8Q69h4TEiVIBHp20FqyFf3Wc3pbOHbwyx+CljlksmVSAOe0RbVKfUNkdvCz+lO1TKrODl/GNtA6+yX03QdIzByYa2/OOiXXv4MWBpe4jWlmYMCypZIAsR7RJvWUjgPeDKuAxf6Tdwcs4n/xakznllVy/w2FfWf6umcwOnp57SE5+0Qp4Wcjbi8Ej5B8yiyFi8KqrtIDHMvSkfJFD3JvM9eMBDzF4RUnBM3smCkUn1XhTSfhADF56pQU8mSzhLHFySd0vJoCHGLwC55PrSWDFOkj4cW96kyxk72EW8GjCR4YYvIxZtIcWEQetZ9nBK8QMADxtgOfBv72+M/1SQNtR2bZzm3kgL6iSvX7VPFpnKXkmhyzaOAigcYCiF9g6ZNHWFfAifjoSt0eLHi8tObfYeMlCWNy1aVyfaOc2TQIHpEfXvfF3P7es1Vdmx3/lb9HxiEBVYmKDElO49mnxPczWLFRJ+MjliHbQ65xXLex7rX+yHbYqK+lEBMDTA3ieP+ix65F+jRNN/19+fTp9x6Kq158BvIJ7xDZRwZgdyI6ZX89MX9cRCnIL9vIdWvaJTsB0wqc/6/QG5yVeXPeqWgevroAn4acjMW1efTRBLN3EH8P3mD/cwB9Su4MJLdAgzWuW21mblLKJG//ZOLn1JetLmWNRbffAKWTMAG8uax281G/ZZOnvKhAUd+RaxkKrADzx5Co7sYp3fslBnp0s0lw/HH/DnSygcMzWxPFhs0kOQfKDNsCj9xDtXUoXc3cwOpE4Z0w6WWwD8PJTX+F5pPFTUrLErD+6d2RqwE46WfSvmIhfhXywEidE+OM808miq6+TxcDtfCi+h3kznSwgAF7hz11jL9qsLy95JVhAuXjmoKhevlOeqVwvWmh2UaUgtuheP6dzfAJ/7OfdixbS4wGvF+3atQ+K3G31etG2CupFC8CDdCvasaDI+/COihF/VznPFLkz4h0VC5IwAHjV8ZMXhxfT5SCLvBZoZHkX8XeVmVMez9HC1Y/MtXqbWYdoKzPPM8nZvAC8igFeUwtc+m+6xWWvsmSPqvRohW/GnhlPbrSvaFFgwyBT1jN1ALw6+4z6SdSPNo0/aLcL2Vp9mE9KwACeB9ovdSZapIHMjvvJOZldRABehQCPZgu2ifU82uy8626ebtDb025RgBWWw6jg7l1TfRN6pqBj2qQSKnUDPJr5ZxPrWcRnL6jP6gIAuoHM98fKk6rt3gXj/HRSLWPxRXetf6YJoKcKWLkAJll+IluLD4BXEcALC/7GVG8vOs7I6DMgKw/yLl4b96VeIeRBFWPvOKWOGuObKnmmyoAXFgOO8ZnuuLUi5cXijf0UV75CHRTIfV1JQIbnk/hx9mLT6g95vgec+3n2pBV45hsnJgEEgFdhwGPHg9F+vvQtKmx23qDCu0FRyJHJaw669sUqHs2yHSyhbxoQlyVTzFa7Z5zOBVXPVBXwWHya57MApKnP6M9aHgDUq4gvXeB9P6XfwWH+qBIQsR1M4riTcd7eOL4cjnO7McWafQ+4n+qMx0zSptP5yPeMvO8AeBUAPG+BimnNlHfrrDIv2E5vcMrIQt1zTlX12Qp9E7TPaopvTHpmq+espHmuVQU8utjFtfpSadNWxQWe+inNWKX1Rxk+M2+cfciLLy9SZ8hzelsrJj7v5prvGeVOLQC88gOeSH4RYLTOguCbyi8YNcyi9QtOF5foAhmbT+7qTECBNH33AXgqE+Wf33/TevN/fx6N3i/D/YQ7eOisAME3lddf7Fc/t8i57/QDnjdv/Xc8b/3RuM+8UjXuPRTxrfd8Qnfw5jSXkIGya9N+9XaLnP2WtkID4FUM8PyAV/l+vxAE3wDwjPsMu3dNmE+eYvcOgAfA06h1m+xUtS4bBN9A9QY82p+1aokEUKr55DbGGYAHwNM5cF2yjZ6oEHwDwCsj4Kn0yoWqK78HcH+7yNZdEACvVoBHg7HjsiMhCL4B4BUNeNRncdmWUM3mkw37NMYZgAfA03kPBdSBg2rg3aAWHJ4FAM+Ez7DoN2M+wc4dAA+Ap+v6rn2W2Os7030AaSsq23ZuV7GNFmTgTbtnn4FvAHh5A17EZ3NRn9Gix0tLzi3T3USgPMfZ3aEZsxhnAB4AT8dAuR03aFV2GCfEVUFxGvQ65+EbAF7egBf47EDgsyvY1au++v447/PHuX8Fu3oAPACe4uQ51ftvSuSgSZ0sIGnfrME3ALy8AS/w2W8in9Wtk0UjYcEf518TxrkxnSwAeAA8CIKgWgMeBEEAPAAeBEEQAA+CIAAeAA+CIAAeAA+CIAAeAA+CIAAeAA+CAHgAPAAeBEEAPAiCAHgAPAAeBEEAPAiCAHgAPAiCIAAeBEGG5pSlV28B8KQnyo1jbau9uzEaHcPzgCBIpwZe4/bNbf2At3HMtuwnG8PhW3jOENQcbXbJ1jvd/rb16NEcAA+AB0EQAA+CIAAeAA+CIAiAB0EQAK8OgDeeKKcbt6M9CwRBsoqbP8aT8XaegLc6HL6NeQuCGjWnAPDUJkprD309IQhKK7pTx+vdmh/gWS/RJxaC6ikKcq1WfJ9gcvLyVQAeBEEQBEFQjYWHAEEQBEEQBMCDIAiCIAiCyqz/A5QRt/tcbyDUAAAAAElFTkSuQmCC)
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Question 6.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAAlCAYAAAB1YQYxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOeSURBVHja7Zsxb+IwFMd9e7sfFWa63l4M600nsFDXOxUipkMMqLJUdcjQIbCx8AXYurWf4Ibregvf4KTyCehnoI2TGEwaY8dJSsx5eNKpTRO/97Pfe3/bByaTCbBmtqk9BMAnajZghkIkTvMKAvDiQ3yFretbGzTDII4ddOnDW1OAocEXTLwLGziDIPYQnFFopIUG/mpc1VB7PpxOT2zKNQSi5/UrdQAXKiuPW7Fr5IwvbWDLApHgCwjgPxlEHnb47/qfvudVbHBLADFaXa+ylRXAhviRptnpdHjSrqG5hWgYRAoOV8ET7VwDoKg3s4EtGUQVWRGmXl+GVPGTqPHh0y+qiRukUgUnatZ4y9Mn4uBOHYJFVukm/MV1C94qQ+zib5g4HQTAM0C9+2OAGIwTgOVWXokllo5PUXzXeehvKUQplFhNxBA+7muGTIHIBXlrgljo+pQm2xUPEdQXfdc9c93h6TFATDvG8kNUqHP8rJUNSMVhUR2S1aa8rIfAfRBc2PiNHdLJGyIbfxyirt+5QMxzlke16JmvRUHnu1Ojitv+i5q01c52I/QzzR7ZpArRI91z2sgE76bv7KNBzD8tv6Wz8aMhMtmS9P1w5qJll3jnRafU0Wj0xcHNmwjoK/2uCKSKTwwGxI5Hn+OAblairt+lhMjrT6ZVVZqmIowfR5bGJohnLJZJCkDH79JC3G3z0bLRgA+q+7JJ+k5V88nGkbQapSUi0tHxfkHU2KT1u9QQeUdVx5EoDQSWpisM36unE0Ww9nWnafzODaLq7NaBWK1W/x76UHojpTRWoi5EVb8zd6dcDl/vK/5a6TTaSCBj8jn8xuEOpYOAC2KhCjFeU4XpNMHv76O7emEQ6YExC2xS8dZux/3nGrDxwCbFZn9WYaIUox3DA/IMsuldTeXhsiym43fmHRvVlJNWYrCTEdHEKkpmUFj0BsOP0d1XGtiw7YezpkOusvi0syhc95RKjDaqzTe60P85W3n7/KbjKhaiwqGwcjseaz7eNyxwVURqjS6GMbG/pkBlE0Y1u7BrLuy99FvUjyZ2bujf6vqd+0pELTIoYp+xzHZon+StfQqIDsa/juk88b+DSFeuihi3ED8QomiXQQSQPkcbAdftn7Va5KeFaBBEvhgX2XBY04EYaRt7j9RAiEx0HurUwFpGiFTUBttAqDcbesOKvUNqGMSk2132f0EZuBK3OwpwJRPt1gxobKxZiNYsRGtp7A31udSB9xVT0gAAAABJRU5ErkJggg==)
Answer:Given: ![](data:image/png;base64,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)
As we can see that (x-5)≤0 on [2,5] and (x+2)≥0 on [5,8]
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ I = 9
Question 7.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 8.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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QIrtN+3DXXsXvs//KjywuX//OJP/7IelKMnyZ4iLXi2gsAUOdvvIpzn+flONqyz33WsZvMZbrOE9nYjnVOI7NnqP0MO67J56EAAAAzCHUZQ1FcLHYhi1QtfZr0Fr1267DltF7BgewAACA3l0RD6DTQUiJRcBwAAAAAKQIAAACQIgAAAMjwf77lQ85QX67+AAAAAElFTkSuQmCC)
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)
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![](data:image/png;base64,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)
Question 9.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 10.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYMAAABPCAYAAAAJOalpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA13SURBVHja7Z3Pcxu3FcfXPic5x6mhm9NrTJDH5uShVrHdmxKvdnypHR00mp3I0gwPnoTyzZMfvccnO5c6nenVnYnTWw+1+w/UY+sfsPQv2CofdrEEVwAWIJdcUvh25jPjhuQKD/uAL/DwAEQPHjyIAAAAhA0qAQAAAMQAAAAAxAAAAADEAAAAAMQAAABAWGIw+t8FHXACAAAISAxSHj0edf7vJ2Dx8+2HDz+AIwAAIAYBGPnw4fYHWXb48TCLr8bJ8PPdPtvn6eENOAAAAAQ2MyAOU36DRABiAAAAAYtB1ud342x4dYtHTyAGAAAQoBgMh7cvdSL2shSDZHgz6/e/vD0cXoIjAAAgBqHMCmJ2Ty4Yi3/TAjJPH8MJAAAA+wwAAABADAAAAEAMAAAAhCMGpt3H2IUMAABhicF7G3AEAADEAJUAAAAQA1QCAACAsIzFOgEAAIQtBnRYXcyi5/k6AT+6PRh8AgcAAIDAxECeS0T/FsdZX45/x/HVAAAQmBio0FHWLOq8xLlEAAAQshiIQ+s6zyEGAAAQ+MyA97O7cAAAAAhUDCiTKI3jO1gvAACAQMWAhAC3nAEAQMBiUAjBAevvHtC/B4Pbn/T72ZdwAgAACEgMRDrpxJlE7FimmgIAAMQgZOOxIxkAAMIWg92kl7AoOhkJwSmFjuAMAACIQWAcpvyGEjI6jSJ2gpARAABiEBhbnP1EnT8dUTGaHRyvdeOfkWoKAIAYBES++5i99J0JYF0BgBY7KqztQQwaFwNxLhF75SMGu0n/OmfRC+xPAKAdKBuQse4/N3fufxqi/dRvxenexjS/3UvjjWs79zt1YhpcpRbrBaeuHfsw4TejiL9JsuEVjFYwMgzZ3jbLREfQZ3Hvzlq09j/q2ELyH+qzenF2Z5byb3H2A0+GN23PaM2h2krr9BED2yzi/s7mp+t87ZHvLAP403ZdL9pfl9W3aK2Nki2m6Ywba7+3+XUanLneRyI2m45m9h0WvWT93f1VEwTRB7GNp9uDwYez+CaJ6QZjT23vbuHGZTG7N87iEbxfZPhFigE5Rt136egK3b0HtO7Ao+gNMpEW0BharmvqmKkjKf2VdV72k93r8+pUltm3Us5+bHuzpqwf13Rwtb+Rpw+siu9TB77Oouem/pF8k8LXim/+t//Vzg2TjUJIWfzcKCxtqd3ohR5Rw1r0MdKig3cQA3Ez2uXod9MlOOXnEIOFNIo26vr+zrUOZZtN7lzPGx5Nuc+bvSs1OOBbT1w7dplKvmpiIMpt6LzzqEX0VuebV5Nv/6yzs6i716ZwUSNT6Clf6FEbt41JMSBncmuQ/MgkWFs8eoIGu6gQxWLrWl6TyuL0O+mjwyy5Ulydemrzi1W0F2KwhAMg8jWNnYpvDqVQkG9usOi3CzXX+pa3PGoEpoGQi3v8bpXEwKVBmj73WReZJhbt8mzXMlQ/144YDM9aZBzd9i6mtbVu9kqLdm2N2tvwrTpf0D2r+t98y+XrT8WI+LhODNRn6cRgGXy6zv/ITt0M9HA//ky3oDy+5928rpOvubDj0efcKga6CqpDHOvA4l9NcailFQOHvy2/a4rZ6RrsYLD9YRr39sbhBXbMOlt/1dUPhSGKeLT4Hu/vfl3njBQn7DL2TE4N1/j6o+qzXctA36OFSvEdxl8kO8nnnKdD7UhsvMYjQmyV2Pbc48imztHVVqrrIr7qXNf2six+ZuDrWz720rPj7trPo8/e6XxBt6hdlodFr6jTytL4C/k3TeWSoQo1rOHjT7Jjt4XplFi68Os05V+rYlBThteyDG0ulOd9j38Z8gM5zQN0KTK6WdJZxZ2MQbkzqnTXHGAfMfAVpybFoC7zqNpgy1EjxfmKZ2dp75aon8rUrIhHn8i1C2pI8qwk8X2ePn6gj2Gf9NLs1sQ7U2zxKQOVX/59+p1wJM2MqfysUm9yZqhLu11E52iw9auqrUU9Vev62FbXteFDj980Ya+rrZUGL+ylPPM6e22+UKzxyU6yHHUqJwGf0qAkTrMvRLmKRVtTh634E5X9X7Ls0p9s/Uj+HXMnSUfTiwVmCqGM6onCJ3KRVe0AZRku6Mvwuu39DEWnfuQTdRmHlhLjrKnsMzpbvxjFYFaoEmUOcF2n7CMGSjZALSzO7rk1MjcxyCvOvMhdbbCFmp8ZveoWrXWjS9uIc9wJTXbWeYbHaCRQ/Ma1DPIdqA1W/Deefmd1tGLxlEaFlKq2qJi2TgwcbD2orWvfEKfwCf5i3okPBt86M2Iu2sfEYYs6e22dixyVqwuLVV8whSDK2bPqR8ros7bj8vSnsv4N703YXhFH2YdUR8N5umX0W1s+XV83fv5Z1M1/bL8pZ2CadYNGjZBTuMvx1qGto20zTOQqBvJWNJvAqA3Wln0kR6byM9PitC0sJZ9hS8P1LkPRuF1TJcdTeX7U7bKnrinBTczujCPlGluzw+xj37q22UG59rbfNDWT9fSt47PvdbIjsdnr6guyTK5iUBfXn9afaACky4gxhUBsC8jj0JBfGea6XmDpsG1+J+qlpvxqnVdFY14xeevegWUXgzIWytMfXUdvNpvKz5QOKR+p6RqWfmHSZbOcbxnK8JHIUWavesluUicKshw+juo1uzOk/FbFwMdW37q2+Xbd7LOw9d0stk7hW28cfcsYiy9DThZfaFoM1I5aDdW4jJxpBF8to6nTr8smmqYMcxUDVeA92hj5Zl192xaZmzUi4TcpVNSL02+amhk0vWZQJwbllLmf3a17nmuD1c0ExPcpltmN/0EvXCx6ib0X45iwrhO2Tb19y5A7XnKlWDjMO4LO1i91jZcx9u9F3wPhIwZVWw11/cZU1ya7ddlFi7DXNlKs863N7e2PXO3V+YLaBuYlBoU/eaV+igEbhUh5+lj+ZhYxmKYMyyIGPsdVOIvBNNlEEhICqlCXkdayrxmIxaW49w3jWz/ZXoZ2Kq8ZbZb2VuL94gjtwglFZpDlKO0y9GGJI/qWQXUedaHNvOPxWoe2xovQS00K27zFwObUOlt96lpX97q1lHl2Gmd8y8PWaew1+oLSyTceJiqOWqj4E3cRAhItmUhRdooibXJkb0XErGEiedzDcPuSTxmWRQykb+pSfqcWgxmziU4pm8h1UW2VUktdp/KKcJ0ZMcssILWTFQ5aNBaXGY664EbOTk6iCrF8tmsZ6Hl93v9Wk4WiXZegLI0u6z4tR5+lv/gvwjYhBupAodrI5c5haYdvXVdnuzQoGH3vovobMdrm8Q/z8t9qx+tqa8Xei66+ZfCFiec2KQaFP/1N50+bg8Ef7HWjX7dRQ2bqM8owUOfWSCT+fvFMGQr/He/qNZfBZR+Lz2e692KL65+Z0Rh8s9uNv9cJiW1xemanpbizUFbHRpEX9lqnPI5iAR3JtGJgyyYqUtiOZEMgu5QO+72MZ4pRjCYVsUzV1EA52tb46sT32Yk6/XctQ7mLsZj9yAVzNTNpYiQ2+n11087o+weyLueZiqera6utIr1ubGtdXZsasHo1qva3DudbNWWvq63T2OviC7oy5Qvq+Uxb+oYcnNhi8BZ/2pe/29wZ/NHaJg39RhlJoGdsb39UCX29l8c71Jehry1DcT7TiS5tVp7d5POZTuRdsolEvztOF9b55oHlSIrms4nyWFv3mU+anS7ss8gVfJ8dyKaRsm4WNZmjTS9efsaOe3G6Z8wCMcy2THUipoXlZqJ8+l/N83cpg3C4OP1Lll37k7pBR7dnQMknL+08+x7ns/HMVteutk5T18WCqmUheK72vq3xrXcz+ValQ6rzBW2Z4nQoxUkt55kFdM3ZOoU/vdP407u6+q3bZ5A/q3dHlpf2P+SJEuytWldJpQzUcerKUP07Raf+Vuczts8Sw2c7xd9k/Z2JE1V1SQA+vmmqH9txHq2umreBjxhMk37oI6S0SD1NeAqgrqe1V2SdrLC9LjuQzwO5MDW/C1rdkAgxaPBsopleiOUIj2GSXF3Ert4QCK2uz7u9PplKK/8eDWcTzS6mepEJcpTY1Kmls6n+aHpKMdrt4SUZa6U4Jh2VILf1A9Q17A1TDMrd0Q3bKcJPhmOxIQZ1YjCnjCdqmOqBc6IBs+4zzAjm0EEGVtd0FtF5tXeaI6xXtq/yvNXNRWBsl+WEGTZQDi2zUWRUHC36Ah4AgF0MQlhTk7ODuruLvQbCy3bT2aqIgXqAFxoiAMsys29utLz09u7Hn9nuQPYTliW7A3lJRhZHrhlCcsGFDvBCYwSgHUTqZ9q7RcfdhHb7GwmCbpexD5RuW9fnBeNIknxDB/vVx6HkpR3LcKIhACFCC58hr6mRIMTp3sY0v6U1JJf+LoiKpO3rcvclnUGyvsYfYR0AAAACEgPNtY1OB9oBAADE4JwhTnAU2/PpLlj9zkwAAIAYAAAAgBgAAACAGIRlsOONaAAAADE4p8iLQOZxGiAAAEAMVgB1f4HIMFpbf7ToW9YAAABi0DLyKkD5/+l4amwiAwCAwMSgeokJLpABAACIAcQAAAAgBhADAAAIUgywZgAAABCDifO8RYopnRGObCIAAAhLDIjy/tSIHYd2JjoAAEAMAAAAQAwAAABADAAAAEAMAAAA1PF/hfL7iYksSKgAAAAASUVORK5CYII=)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 11.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
As we can see f(x) = sin2x and f(-x) = sin2(-x) = (sin (-x))2 = (-sin x)2 = sin2x.
i.e. f(x) = f(-x)
so, sin2x is an even function.
It is also known that if f(x) is an even function then,
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Question 12.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
⇒ I = π
Question 13.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKwAAABdCAYAAAA4/41kAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAlsSURBVHja7Z29ctNKFMfXtybclo9sOqAFr9PdoWIU5RLoTLA1aQhx4fFoLklmXGSIQ5dhuKmBW/DRAHmAW/BR3SbAEzAkL5DkERJydVa7tmwkW5IVSzL/4j8EcLTy2Z92z55zdsUePXrEICgvghEgAAtBABaCACwEYCEIwI5e24z9xn7S9m+wDYDNpCzBXjqQHiv9kH/ymfe1zc0zsA+AzZQ2N2tnbHvjXMs2r5mV1vWGwVeEtTEH2wDYTGvDEnMEKoAFsLlQwxBLpt26VhXsFQHruAUF2AXAZlLN5sKFIuNfNLDXKg9vNwxjfqHVOg/7ANjMyTb5sl5kyZ9p0SWqL2AbAAtBABYCsBAEYDNpFN8sV0ewEYDNGrDH/QQbAVgIArAQgP2ltA2/FcDmRc1mbcLk7AP5rAUmdsvN5kXYBcBmVrY5vUhpWfpZlhpOmh9RWghgcyEqM+Ss+AV1BAA2H8C2Fs4LJt4DWACbmxF22rQXYQsAm30DMVawTHMR/iuAzQWscrfBwsZN/XfYBcBmUhSDdWBd5UZjleKwzWb5omHYd2AbAJtJVQV70V1DwA9u1NeESiRgpAWwGXcNKqLKGTt0fj5Roy6gBbAZjRJUxC3PaHtCo61OKoQFfhweWgCbF/egyLcIUMp+OaPs/lTJfBo2arBWL182rQezKUGWWB3vA8ucLdfXLgPYrI+urYXzevds1N+lnbelkvk4jZCYm+xg3x1Qj7QPHuc7aNHhImap9DjtmgpAOajjZVqWf4va2VQ8MzMlnqeVHduoVK5627aEaA17Lxsr5lXOZ97Vms0JAJtR0ekv5LdGPflFhsRMezkL34FGR0MYD5MY6akQSFRatzIDLOo/hwd2GDfCu8hJqh+STC23C4GazQtRv0sSC7fuaaxevjIjpv6JMwUmvSL12fxXSBNYbjRWIkUVhixHrAr+t+N3HibRD7Yh7ifVn9KXnWQfw46y1G/1eWOuyNmXKDYcCKx20gvyaMn4hkoCrPZJKzKE5B51qdOjoxalZqMAqzuUieqrYdqtCP7E6Yf9YUFL0h3wugXygQzhy9Y9fZkosF3GjgnsWv1GURj2/aSmHucB2mM83TpUDWxYAN0pkx0m0TmJRQuEtZ68TcIzEmeWCu3D0sFncYClkfVukb1OqqPUiL+XdqV/ZGDdJMNJVo7n1EeGnopfH9ItSA3YoEA0U4UinrTl0MerZw7YkPcR9oHv9c97XSm/xa938dLj5xeCp2+x7jdDBa0RwiQa9CzS7yH2XscP2LjthzZ4rVY+a5amnrVTlM5UXa43r5AbMcv5m16fc9iT/vIIbMelEnv93BgZoxVTz2VQn4udSr1y3Zm2W/0Wv/Q7FVMsc86+0chmW+afgrMdsjcv3t2KEhvtXq9QnxV+UAjOk2w46ec/D+obun/n3j67nIgdyxJLXmCHaT8UsDJjw/m/OsXYsiuXnAvvyo5R4Y0kh/2owAZEFYIUaVHo2iMcsO17HgBs1eM6EeRyEaNGKwrO+y1+qXpMd/BUyXym+0ItUCO7INRu+5qTxicNvOvSiO8Vu3UpTt8QK4IVdrlprdP/SVZceLvYiNt+KGDp3zpTvSuPC7CSNrCeqMJARQ3mJw2s/gwdkKwfnt6FUdDiV4/2Xjg9i7zVOBGEWc7e0zXpfmgWdWbLt4PcGfUddv2+Jz2MjJsfvLYKirTEaX8gsB3jqam+V2rqTxPY01QkYLVv1+ez0p7yvAN+aMzX54JGfb+Box+wccNonWlY7JVK/G2Y8GHQAxUUIenHRtT2BwKrwRkEIoANB6ycEazp+fbrlDh3fNJGtXeROipgPX3XNTXHATaIgUFsRGk/NLCsWH0d5D/Ch40GrF4HOIvYp21wi3dfe+9tlMCS38g5/4/8yTDF6SGAXY0CbJT2wwIr/ZXe0jLpYKvV7bj6sFGiBGGB9XaIWpTs9II4KmAp2cP57Ft7wz6nXRXaChQL2AVx0334uge3IJA97b+h9l1/tn/7vivY3htRbwU8Ybz4lUJZ3oWXNl4vsN5O2Y4xuuUxrBVm0aVSpeveqU92mgNdF7A+/ZA0sLSxssRLb/S9yvJBxg78Bqcw3zNocNPJFHcW6bg+cdr/6Qu4N+Ku2rpWsW58TMXNdLxVfNeNKcMd0E3Ras8yzXvUwd6nURiNpVDZDKddpxOFSs1+pZtPq/glSqYrTBxWL7q4sJ6Ua7Wz9CDXZcSlY0u/fqCH/q6EmAaFuvP5E5k8eFi5dtt9oIxPdL3wsNYmjEn2SV9L272uoj/yeu7gVIgymLRrB9z7+V3uuHDj9y4z6s08Mhbt2Cpq+73T2X7Q9ElTlydBcOy3TcSSBRtusFjH0ejLzbihC+f3xG6YugC/KT7t4pdEgTWte7Zt/qFcgSOvvdQo09MP1rqy4VHn3+rLyk5HnWRO+Hfhql3BR/paHtiOPDuFfYP3g2Y/vZWIrkUxY3eRyfenTesv/fm47Y+085Ooes8ysB33KZmywKyq44ZYL0fd9mgacYb1vJ5PpX3zsMCqhUdmil9O0yZpfMdTb0CmHh1/Nq2do6MG1hO3Xh1XYFV54UEas8hYGvQ0pr9IBdwUHhqygDvLkiG3nvQrgM0psG23YExP7G5vkUnJ5QGU4ab43aibEAXjn2/U14rjZg83Ziw+p7V4BpQBi0Sd6HCneP4uqr8mR1nHLRi3M7jIf01z+zoA9fPRinxLBuiL1a1as3YhzoEYqrD97TiNsrIuesp8lqarA0ADXABPRu847ohC15JHFaV4UkpysNYm6KiitOPogNRHnUwNZWeGix3LqqychvS8osPg+u1CALAQBGAhAAtBABaCAOxQ2vbdbrONUx4BbDaldl0ct/dgRaw/hQDsyERJANveOEd1BWaldV2+bG6MywcB7JhIH6wGYAFsLtQwxBLVFFB5HQGLd3UB2MyK8uj6GHgCljYHNgxjHq+kB7CZlNzwpxZZ7c1/Q57QCAFYCMBCEIDNnLYDz+JCcgDAZkwUZ+0c9vHzcaKDDpiDDQFstow04IA52AjAQhCAhQDsL7swgz0AbKYlN+HJA3/ZcYGJ3X7np0IANnXRxkR9NkH7XasoLQSweVD7FeyoIwCwuQBWnl0g3gNYAJubETaPZ90C2F/RYIwVLNNchP8KYHMBq9xtoN63gAJuAJtZbavXPOl37tKbXgzDvgPbANhMSr315HjQG1YgAAtBABYCsBB06voftHsq6OR5g+8AAAAASUVORK5CYII=)
As we can see f(x) = sin7x and f(-x) = sin7(-x) = (sin (-x))7 = (-sin x)7 = -sin7x.
i.e. f(x) = -f(-x)
so, sin2x is an odd function.
It is also known that if f(x) is an odd function then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 14.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
As we see, f(x)=cos5x and f(2π –x) = cos5(2π –x) = cos5x = f(x)
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)
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Question 15.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATgAAABPCAYAAAB/L9mnAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA2cSURBVHja7V3LctRIFlWxbphtN5DeMWyHSteyWRGyePTsPFhWeNNE16LCoWhsR9SCAMOOiKbZA4uh2bRnPqAX/VjNLIAfmCFsfsDmE8ZmdFOZUkqVqUdVqVxWHSJOBK6X8ipvHuW9eR/OkydPHAAAgDYCNwEAABAcAAAACA4AAAAEBwAAAIIDAABYDIKL/nUinMuhg8kEAODME1zAndcRoR1LnAgw77f+06dfYEIBADizBPf0af+LMHz85W7oXfP83eubLtvmweM7mEgAAFqxgyM8DvgdIjYQHAAArSO4TZd/54W719a58xMRHHxwAAC0guCGw42LXYe9TwjO3/1m03XvbuzufoUJBQDgTBNc6LEtdagg/k+HDTx4jckEAKAVJioAAAAIDgAAEBwAAAAI7rQHO5rBkAEmFACAs0xwx0XAhAIAABMVAAAQHAAAAAhu9qZqB343AABaR3DDYf+8x5zfYr8b/7gxHF7ERAIA0AqCC73ePUrTov+L0kmXvd9RKgkAgNaYqApUNok53feT5qEqkxcKAbRugS+4bp9tgtvd+Io7/NdJCW6dsx8dh31SO0MAaAsWXbfP/A6u54X3Jv2dgLNnkRIcguCAtsFfcN0+01vvwPPuwf8GAECrCI7ITVTz3Xh8W/2NyWyZYsa+I8wrsFgEJ8lth7mbO+Q8HQ5XL7lu+LcKiyWJm8svHJMjVvtOJ9fJq1NyLWPHr1nmzFYdr6FDWafuvWtKZnqARXO8Pc9yz8N8z0q350GvF4Lgcl21jsv8CxQ3t8KXXorPMv7OH/jXOQ921fsPBqt/jt5/xRz2Qf0Ofcf3+BZjzgeqGBwG3i3OnLfUwYt115/3h8PzpmvFhx7Ovuz29Vl83gu35OsH8WvN+kOGg9Wry4z9ou7PEl95ZRpvIqPjHMr7eJSXrezeNSlzXYKjeczLvdrvXzDJHXi9+3m59c+KWMvlpRdFcuuyd8yy7zc932XjrK/ba0bdNsoZzU1OzqN59PO1wYwpfPpQWXO1UKgrlyBIvv6TmLjQu5YuzvSkSZKomMylZe+FF9y/Sa/LCsKfixrdJNeg71/2/lAKs+vzbxyHH/jh7pWm7seDwY1utHCPekF4V8lHf+djBcXCuOz8rrdbDIPe3fyYi+5d0zLXIThN7rVZyq2/Lxb/ZTcv+36T8100zsfb3l9SUkp1O/rO3xVRRQ+Bl14Q3srodkR6NjmT785YzoUkOGGq+j0/UuRPNDFkslqePB9p0hQBitd48EifOKH0uaN0WmB5MpML51PZwhO/GWdbCIWhhXWTsb0mn3CJHLny7fEJMd/XQ2nIxDeFDiglp3tZ5d41KXNVgqsp97Zpp2GQ+6Cq3GoMN5nz6yznW43zmv/wr4W6Leaklm7vVJGTrjsLOReW4OInR9L82bhF1ifY9Tdv23Z69CSsowS2p7lJASmdbHmZ7VVpb2jwDRUhI4caW9l1EkIwZIAk8kXvhY/DL5N7d3dwp4r/cRyZbXLrftZ5lztrqs9mvjO6XTDOaev2OHKC4MbanrMfadIodYv8KWRKmkJGpAkSEyFjH3r+pp9XhCYITpgJAb+TN3+KkDTRqQDy9Riu9blM4dTOzLjQ1XuU4xvtfKrcu0llLpD7RCLzel6+RG6LaVVD7gOb3NzfXI8u0ak+324D8z3YKtNt0zib0O26coLgxtieq9aBlT4f+lcSZyzt9rrrb/SF2hTB0S6TMfZv6ZTdafKeqIVedp2ihZ6a6/FCN9+7tTdFJDctmauaqDXlPhBy5xalJvfBuHJrsv9LyT6LMJeycTZinZyCnItFcGIy0pOhMjNAVwbOnHf5yW1CCYTjm93c002eG4MH3WbvCfkjRyus6DFlummTH09CftKfVeXeVZCZN0lwyYFCs3K/LdsdT1P2On7osnFOW7d1OWN/XPNyLhzBVTXHSKld7j7Un9jyxO1Tk0pAzamX2fJeuhuwL8JpQXfy0w6Vwh6U/4aeuLoc0jQaefqq00gKoDbduyJ/l5T552nJXOuQIZF7bTK5o8/WlbtM9tXh8FJT820Z55FJt3VST3RbM+t13bbtyPJy0kltU3LqsXpTJ7gyB6fFOdqZR4Ij5Wc8eEaKoJzXuilCgcKx3ymecPXUX+86b5Tpo16TBxufi/xLKhRBX0QqOFl9d3UwvNrIfdngtxNTJQE70sMicqRwIv1q5/r91QviNbmL0e+dIg157/bzxQ2akLlOmEgdueUp4Ensr6os97ZJbiX7SqHsbiPzbRrnIDdOXbfVaSvBF6RHuj3YIZ9dVrej8faHF+xyxt9Rcg5yck6DB+IICfd29NR5XzfYu5TgKFCUfjhRFNZ9L08gOwbnqFKoY5U2NUuCqxSu4QXfhuGNr+X2nQIi36qYHfnUOsw6c4NHaUHN1KE/4hDOLR4FPRBZHQSMOpObC/4UsX1KVgp4XfZemGKU4rgpCqVIx9Tzgu+VTGX3ToffgMz0/fxByinK/c4W50WxYacx32XjlLurEd1eiQk+c3gxqtsrI7qdkdMdiHU3aEhO7Xc/T+q7HrWvxZZz5DRr5JRKBsl+JAKctFzROOZLFYIDAOBsQp3UTo3gki1vxPKKvcUJjTRl9JO1jGP2FCrqKoKrepoJAMCCE5yttpot0h8EBwDANKH79HWCK/L5lyX7V7pwfBIzhzs49GMAgFaACgPIMCThSwwC/p0iOHOy/6BSsn/phW25fnUIbpKUFBAcALQbFH5CQdjKPabHXCoT1ZbsH+/07Mn+FZiVDh74u/xBQh2CmyQFyb6jBMEBQBsg1jNFJWihV3rMor7ZolNgIrmqyf5lNnGHcj5NISCnaaKC4ACgHbBV6LEdMqRmabdSsn8huYlgS8uOat4JroZJDABAA6iyljUiq0Rw+nuxqfr0/FgERz9S1LHqNH1wFQnuGACAU0WnBsHt1CG4qsn+RjIiv5upwF8muRc+OAAAJoRMszvJV/ixEZxM9v+5arL/CIGJUijd9ef5nRWlcHHu/ZAEASNMBACASX1wWi0+PWE/MUNF+ad/CnPXkux/SP44W7J/1uemlQA3Qe2u5C6Pq1Qt+vFZJtuD4ACgPaDc0w5ZcCLRv/8niomTNe7ioqeUGzvsXyxI9j+xJfunZmRaHdSCNJHWZHLOMtkemQwA0C6oytxxoQT3RcRHa7IQwn3axBQk+/+vKNn/TN4MEBwAAFUAggOmq1CGRsMAAIKrAVUPDgSXJZV5qI1PgeGmloQAAIIDwdUmtsFgteu6/BF1Kp+H+nhxMcnmCnoCQOsJrmoD5rZDxBAtLf1nacn5LwqAAgAIrp1EV7GEu8W0PXWzFgBAcDrBySDjee+qPe8EV6exi0aISZ6hiRxNhwy6jzCXttcpuNZYBQ5NYy25TqcsVbCi3BONF1hwgtMXSVxenf0Dfp7ZEZzoqsSXXibNTQb+dc6DXf0zFKAZfeaV3rOWvud7fIt8hNTXIwy8W7JJygllzJi6kxkLHHrhVhr1LgocWv18NI5lxn5JGtDwlVfUecokU+D17qfNWdgRjUn/rOgYphorW+QuGe9+2XgBEJyz3mXPxSIWi6J/cWWJv5x1s5tFJjjK/1WfjTtTOa/1Qx7ZhGg/jj5PT1Flxy2x8KnTlRfcv0mvy2Bxa+vH5BoiSj1t0xi3t7MXOFSNk3pBuKa5M47yWS+q1aHeHU0Gu2euVyZ3frz5goxl4wVAcE72yZ0+ITGBsyG4xCUg+8Ymr+UKMtj6dxQ10S66vtbHVHR1KytwaKs+HZ/sZvuaxmMaLXOtiFcrlX2geora5B53vAAITlM8lcpB6Rv2Mk4guMq+JtHIWZabKSxZlTaKZp/cu4M7RX4t1Um9KsGVhfroydhlBQ7LOtCPEKEhlzkZV/QeVayoKnfeXK0yXgAEB0yJ4Cwlq04kSvOKtVzlE4exDz1/0zct9mkTnCZfxnQsug/5Hr62HamR4DRCpR1fXm7ub66rZO/y8bqF4wVAcMCc+OBiUvKvJA53chWIUjZZkmuC4EQJrwoFDrX7sFNpV0gElyOg1MzmB8qkrSL3OOMFQHBOgcmFo/cZElym2KnW9Shvgk2b4GSBwz3dXLQVOEwOFGj3NRxeNJjonbzJHf1W17i7k348g9xviw5H6owXAMHZlV4oMjvMKygIbvoER4Tgcvehvtux+bumSXD5Aoc6gZkKHKbEFe+yKNxDPQhpV6VfX+/apJOY0i36bB25xxkvAIIzKH3/vIqBE0/bpZWXi+znUIs3XtSi7HPlpPs6BEfEwXjwTJHGpig0mD2ZHA5XL4ndTzQWdfJIWOs6b5TpqF5LxnzZ+8MWo+aJAocpAclGSDvJ9wbDqyNkH5fAPs4Wa2VHejiIkkmeeJ7EfjXnXL+/ekEQpNy9WeTezsutxrtSOF7XOF4ABDe6W9Ge+rRjWNSTKrlDOBynr4XaxVT5rFjoXvBtGN74WppoFPT6Vo/tMo2FGvlKEsmMbeTAI0c+BBk/l5Fn9KDEHDwrYvLUOEUBRe+FKQ4tjl2jEJL093pe8L0ai0Xud6bfyhRkrDleAARn3XXUdZQDAACCA8EBAACCA8EBAACCmxLggwMAoLUEF59+sT0KD1ExR2gdCABAKwiOkJ7Y4VQKAICWERwAAAAIDgAAEBwAAAAIDgAA4Azh/84QDvBSnZsVAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 16.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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)
Here, if f(x) = log (sin x) and f(π – x)=log ( sin (π –x))= log (sin x ) = f(x)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Let 2x = t ⇒ 2dx = dt
When x = 0, t = 0 and when x = π /2, t = π
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![](data:image/png;base64,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)
Question 17.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPsAAABDCAYAAABa63O+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAu2SURBVHja7V1Lb9xGEu5RgFw2To6bOGrekuzeounRbTcnY0StlAB7EGwOISwQbwaLgUDYloI5CPHINwGb+Gw7hzg+rB/3+CDJp70k+QFrJJJ+QGT9BNtaVpM900Px0SSbj2Hq8MFxPMPu+ao+dlWxu0hu3bpFEAhE84EkIBAodgQCgWIvYiKEtFzMwZ9oGARCSTNzaTRTC5EP+/2LPUa/oYScsPWdFTQkAhGP0Wj9vTYhv1Laedq1NlYIeTJXe7GPLPapQYzni6Z9zXF23kVDIhDq2Ny0PjY7xh3KrG8IOWvVVuze3Yn+bDqjBTQcApEdNiP3aXdjq75id1d1wnrfZ8hR5tDAleWHyH0dw3rHXKDUfNwfDi/UUuw9Rr5370abKp8dDtcvMkKOXGd7RQg7Wh+N3kMjl4MA98fIfT1zeEbY3vpweLG2Ymf2zqrKZx2T3qCmc6PfX3vbpPQJhv7lYSBxv4Tc1xK7u/23XF08jrPNzIgdqvae0Ml+i5DXqt9DaAnhkXsUe3li5/k9oSeXHOev5jw5QIcrMURE7lHsZYodqo0L1lef8RUGHM4afYpGLgdB7uG/kRcUe2Fi31lnK16BiJ4YBnlOCDvEQlE58Ll/idyj2EsROwKBQLEjECh2FDsCgWKfebFLp+TwpFyJQN5R7KWKHZxsw2I9Ssip+99nSXuCEfqEHuQdBY9iL1Ts3nNfqMxznBFCX+CuruKBvKPYSxd7r01vw49yzMWrcAbe6Jh3+ru7b+Vdtar8/iwAeg4EeL+bl/dZ5q5O826k2HUfiwWDwYkh076+nOc6121z+dJgu91U0RdxHFkX91WhTjZvptjhKB+hv+hyOghNF03nqo5r2Yx+DTv7mih43bzr5r7CaOffdbB5/cXeJg/Sin3HZquQL8Z9L1Axjqwabw8utSldfqQjFBWEL1P6CO72aVe4ule3dfJeBPdVisy3OavS5kLscb5XKUnsD+R/dHV0VafTeRXjRQtySn977emitWEFPzcc9i8szbcOdPe841tL55cO4poIBOc7uNxdbVPys+rZ/krFHnEmIYx3Zm30wpy5KO4r48a1eatim7tp1h///Oabh3/6x+jvtRR7UtgR53RRJG106Rah5j6sGF7oCc5HT4Pj8MryvHmge2XxmgiQI9WDOnBWXFS3Z0HsKrzvbJofR/FeJPdV1jOqtnmtw/isYnedajOKJJ/0Y/nf4K4LDS3lcfjY8+SAMPt+Eb8NTomlceYkIdUBEu9bWXkvg/uqMLa54uqu2+aNFntY7zpVAnm+SMhpUVt1vXnQU9XcfZbEnof3MrivNvKpzuaZxB4osIQWEIL/nqXIoFvsMJevrIXPpJ1dkc0RvWuEh5hJPKg0XvTTh9O4nX3ydcIMn2f8MsU+zfu/vnT/fCNubircq/qhTuTlO6/N846fWuy8xxgzvp3skqIv5s3ejkw0L64w4x7/d8p+tAbWJ4zZoyx5TpbntmOnk8LkSW4udnaR135zxNBz1/DIL65xoh+WHra867jXa72GHmwiN/N3j51EzV0YPqpz7nCw9hGj5CfBoW2zL2TDJ4x/mDR+oWKXeJ/k5mq8q3Cv6ocF5Ny5+PZt/iKLzcPHH6QaP1U1fpxLuYawnNEHPA8x6ShY+YbHZcIp4Ts8V0nRDnpa7O39tE0QwpwuTWgk/864scVv4waY7z4TuZi3ZZQdCo5inOc4bI5ep9bWMTXtm14R0frAd4KpecP4rjC+yzK+vyK0QlaLKLSK5l2V+wg/vBn3JEBXGJyHbwWbH8XZPO/4om4Qx9HUj12iZI/QpT2YEDiAFBbLK84xtCUSDsL/H7NvphY77xmfvkjjrQzZnS7OKGEOsAyc+I4GKw48U01aUcdjhDg13CxF1Tqp6CiPL9pCqYwvVXxfSnvZIwGrSNG8q3If5of+nvzCaxqC71YGvidRn2vzQDtnzl3A5o5nn3M3+KzjC5vPuQtv1JthQlcEGMR/ZvoiePeBDqOQc3UvD1az5FLw+e3B2ocdSp9mCUNzi12E2IrVctmInQ59pPJseLI6TeemUl63qTrvSSinPn4R0CL2FNwLP3TsxSt+qhB7fV2RzDm+FQuJumw+Gb+danwplH8I+0rC3v12jjCxMYIy+2uny/4ZnJBL/mV/RXhNKP3F2zjxRKlYBMazzcXrhtH5QSUsqYPYpetOhVdZDB81v6R5px1/1sU+7YdWqB8WGclM8717IY/Ys9g8y/jyPLod4w4cUlobbH8o39imDdqmt+Vji5F3HzfngJfJjUXfvvIgaYWHO1aHdv5j2s7f8lSSqxA7hJGU0v9CPqVyhlvB8Ftp5p12/CJy9jLFruqHRSEL3zptPj3+4MsM0fMcRM+m0bkrzyW2ghzxSKgli14UGlTCDV70MhevwWtm0+4f156zK77GSOzhdnacd0UKk7QPOqoQ5XdpPSPt3oOIeW/pGL+InJ0XYvXk7EexT0IU/bAo+Hw/BL69eoka33E250U31+aydqJsnnV8OXp2F+K7cOw7GD3HOlywMMJDBNa9KYeSYZskniSsGHCTgJw9i+DjqsIqhRzVarxXRV17341GHorPjR+vuN9dGw7fT1uIkp1d/r6YtxchTVKi4Pj+o67E8YuAIu9beavxCX5YaGecCL5PIH9O4jvZ5u1Em+cZ3/t+/8ISpY8XbedybIEu6Mi8iGYYP4iVyHGsBctxFmB1gXx+rd9/GwTN90RLz1XlcIZ1N76IzYsyPLKLcjq4o12BSrdPoDe/8FqCFx3Eb+wA4rrz5JnsYDyX5L8Xxu8+WxsMP4o1fMjvG++Lhu+7c+ThlnsnHj+npsu8Cj0Zf7Alqqv8AIXC+GWKPYT3d+JqOF6EEM39xMHD/XAwWGtnrfckCsX12yS+IxewBJu3JjZ/57zNl/b6w/5Fb3zYmJR+/FsKT7im/iI6kMADfDhnPKkMun937xZcyKb9ueOYf3HD9x/HG2sk8uE7S97joti3reZ+zi6RGthUMwHrfRd2De+xR7zY4ZnnJMx1bkiPS6Qxwjc6jCuw/vfOjy94Jq+gkOIVPYFz+5oQkj/+SznMPh+al7exJox3aVPNdLrArEiHU+E+yQ8LKkDm4juq6j7mz/1NBiG/wfWMTte3ufGbsLkOeyf1hyjUQWzGRvFiz7GDLkNUEDRMUZs0/HejNao/mw7e5Qiyaa/vqtrmlR2EEe2G4rqQFHEQJh0xZD9YKNO4SpzbRIFiL4f7qlC1zSsRu1dxNz9P6iuW9zx7XqfzqqRqFfn0uV9zGjPo5n2K+8BOs1nF2OYVnuRr5BFXXU4nVhjd4SQP5xq2qusWu9gW2pRQ3rO5V1itWk+1bEvlt9E5imujk6UQkvpa0AdN0640uMOn2cs8Uw6tkXd+84Dinkbuq1zV62BzFT39rsUurgcHeXT0jYcqctPC96J4F4LXwX1VqJPNG9mDbtzvS2N+pKtvfJPfjlIE70Lws9w3vi42b0zOLrfdzXqTQGRbuZD32UBjxO4djCBntN27zXcaGeye7io6Io73K5x3OFiBvKPYCxP7dCsojldRO9MQ+sP2ad4HyDuKvdiVPbh9Eo1bDpB3FHvpYkcgECh2BALRVLFX0TMdgdyj2EsWu98og+eQWTvdILIBuUexlyZ22JYoPs8rxcbSvVnfajkrEB1QkHsUeyliD3a2STqoj9AHj/tJBxT+MgLkHsVelNjhPLW8Lzv4d0RxQO5R7Ch2FDvyg2JHsaPYESj2qcmRfdXcj/dcD+bsDT1OWruc3eXee4eYdxQVua8fvO3NbC/u7EKlE4ROo0m9xuWbAzQJgIb524NLjDc+aFg3mDqvGsh9vSFeJhL7Wq1K70a8IQL7CfqDqzQwmLSMLvfd5Ai5bTRyXyeIF2BajNxPOqhU+WT56k47T7vWxgq8NAENiEAoC31uw+quwDsc4AWYiZ+vRb7hvyjSIMZzXDUQCLUcvU3Ir/BGZHhZqtLNAYlDIH4nkQCSgECg2BEIRIPwf18KG59x1p8uAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 18.By using the properties of definite integrals, evaluate the integrals
![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
As we can see that (x-1)≤0 when 0≤x≤1 and (x-1)≥0 when 1≤x≤4
![](data:image/png;base64,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)
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gSkXf5sILDvIh5SFd5Fzi7MQ94IZEhwAsxDwFegBcEAV4QBHhpBK/ueHwhfsFlKHgEqRZP1KTYG3Tonkp4dUejhemLXRHz0FxjfsV/YAO8BBOZEfIcd7BB8xIvJph2X52KAo4+vMi/kj8TMQ/VMquw48bbm8SYXxkAXhAEQZDhozSYAEEQBAFeEARBEKRY/wcp/uSmh+pYjgAAAABJRU5ErkJggg==)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 19.Show that
if f and g are defined as
and ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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)
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![](data:image/png;base64,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)
Question 20.The value of ![](data:image/png;base64,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)
A. 0
B. 2
C. ![](data:image/png;base64,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)
D. 1
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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)
It is also known that if f(x) is an even function then,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAABDCAYAAADkvSvjAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAqvSURBVHja7V1LbxTHFq6ZSNncAMubYFdnRcLdQdfMLneHxu1rgsRiBD2jUaRYGUWjUSswoFkgMmZnCYU1ZANmEcB7svBjlQ2Q9eUqePwDMP4JMb59qrvn0fSjurvaXXjO4pMM9nTX1NdfnUedOk3u3LlDEAiEHOAkIBAoKATiIxbUOiFlQsgnNko4aYhZQd155stJnvvoX9oX6rfbpxuM/kIJ2WOtlSWcaMQsYDBofaET8obSyu81s7tEyHo5s6AGJvtWI9r/qkbzJ8ta+RwnGjFr6PXMc7WKdv9LZv4iIqrQX/T7rdM6oa+M3so5nFjErKPJyENa695ILSiwToQ1H6X0O23UP0EiPpo4AfmKcwEt4zylxrP26upnqQTVYGTNVmQvyU3BqjFSGtoE/V0ibNgaDL5AMtQF8pUspmKEbbT6/dOpBcWaKxeT3LRj0OvU6Fzvt+snFyhdN6zBeSRDXSBf4lhdbX9mUPosbo6kCgqygu12/ZRByWaJkPdJP484Wnh8LVKygXwpKCgedxG6Z1jWN8Y82UKCFHdjXL4uWNa/kS8FBdVk5NF58/YlbqVsguBnJENdIF+KC2qlxZYgwCVEe6tp5DUh+hsMdNUF8qW4oBAIFBQKCoFAQSEQMycoSMuS0U78YQmJURvIl8KCAnK6JmtQQvbtnw+hDgqPf6gtJuRLYUE5exzkwF7yDoAgQug73IlXF8iX4oJq6PQe3LxrVJc1Qt5qldr9uMLChK5JqehrHCfkwVfWOVaJo0IF5RzOoq/yWOFggm91LuhG89pilutcaxqLFzq3dBRVPnzJ4EkljooVFJS6E/qXbEHBxIJrUjWsZSmrMqN3mTn4dtZFJZsvmTypwlF2QenkcVpBrTTZRfDDRT4/nVmK7lthr3iM0sWnslxHmKRFSp/aqyBL4YqUj0smTISvonhShSNPUGAxEwsKPsz+Qf5LLw2+z1NQhzyzVDXBZyc8GKb7zOw2gsjq99snFuZLW7L7WkD5TWl+Yavd758Q+XsYc+dK7aJOyZ9Jz4sdJci4sU5so5ERX7YlUJGnDBy9ksWR7Rb/81+ffrpz9rvB5VSCEjFvcQTFfZlujd4g1NiElWylZ5yDRjBAVtB9eRZq3tiSZZ0m4wdGyDDsYfIDzhARNxOmoqB4Y51O/WsQvJOts0H1P2tXOhfDRBXHV9E8eRyJFu92DXqtJJmjTC5fVkHZBPS8vYywv3F6VpDdyS8MK5FGtNf+PhZ8PPNkO82RfBFA1bX9EGyLPgSiC0YR4O4WKb1zil4dwFknGG/YAxnFVyRPvufD5WkrD55GHAlaKdkcKSEowhprMr4wZItgwzGvUihnLHQ/zj9WXVAOb6VNapg/e4vDwDLPLLgHCAlhu0HV5FF8qcJT0RwpKygvuL1tnr/kfOEfb8Y1CeEuR4iLAahPB8ujspm6YBDtZLnIfpRFnYhJykFkZR2DlIfOdseqRnc5kE+wHCFzGMRXSp56efFUNEeZBJV1X2JEUIAvDaSPg1sePx44rkn4WRxI4Yetrq5/veO5Nfb13kOfBO//7X8f8lPEEe3QPLLCLCrEJIyWXvJxUvai2WQ/TJLl3utN7BgKrDxw53AYaaEm+MqJp9RzVDRHmbJ8jt+sb6Y9bOZYlGBBJTXJ49U1mCjvb2wyH/LJmq+N/GynnIbtmNbgjEDQuxs03kG/PqeT0i41mtyNAhfKDlJe+seedQyHH6alI5AsFTyObRoPEy+AivAkwNHQc3Xz4gjiuLjkVfDgU/bkm16p5AgqaiL9ZLnNRg7dY90nYf9CpFHn6B6+hwHMP+zHeRmugCC+5x/DQsoxuNnDv0UAK2vCRIUd27AX0ZYlm6CS8BQ4RzHW28v0cY4mWnmFcWQ58ynOkYD3AByVmbkWtaAFplwrmvY8S8dYqYLyTL1AKnZsvvXdSoU+Fd0LCYsxJvz2nujY044hL4Dlg970UeOQIqiceVKBI9fte1I1u2ZYW+bRD6DUplG9pmmV53GmT1VBTVzXNemrJ7IIKmyMcWNPM4Y8wI9k2NY0zqIdtaDSzJEqHME4oNe5VjEe1Dv9r/1JjJFiK7Tym9G0/pP09R0qCcqrIaOU/gF+suiZHgGyboiOPe0YZMdQ43q67nIWvo6Gp87NuDnKl6P4+08CXu90q1P/ytAq9/2u4tSAbQv1E1goqJvKIiq+CSc7hooIdqdiBbr4xFqxPod4yt23YOKCmr4HL3mB76E3HoeM/YasMciMobxKb8aat4NSy0n4SsjTMC+eYjh6DxxNPrN5cOR5ckZFewDHW4I8uYCVxjxTofR30Q20pFmjqcRHTDWFaPbIyUzW52wr+8T7G7dE5h34yfV+fy5NQD1+SKav4Y2d6FcfT/rSIWPYExmDTDcP9o6ofvWe37L12pfPMmbc9XMSxdcR8eTO0WAuJUc7/s+n42gQyRGvU6T0WbVpXUmU5eP92iKqHLIIymv/exUyM+4Xrrfbp6LeveOsoOEbhtCbuzZPtp3NR8cdAhfqxxq96Yyjth3k735AVkBmEywHrwuDa9jj5KbeXqHcOrkDQhc24DtmHYO0mGniGHsQqGFdF+FLNZ7GHH34XI5q9xJx5HwPXkg72uapbV9u986GPicC2e+Ijd1M+1DhpSzjDcNpVyZkj2ScAg0nCvYW/O7Qhy6U9jYscznKFAU8bA5hzilWuA6YeqtZvQLXgxfReQ+g8Bhy3Nx1xhXlLgbfP4ivQnkKKrrNiSMQoyhHImcE862UyGDlAibznWhFeOLrOz2+Z7aHgiy+8uSpaI6UL45N/mXIpj85IAs8y+XbGJwleJugWfnKk6eiOSpUUF6GRZagxtkcfTfuhVdJkdfBxY8JMvlyeRrK5EkFjmQIaj27oOSdi/FKi2S7E9yVoIsbs2qdZAsqD55U4ChTcax73HcYd9w3xpfel31eiKc4oVeB4CEzkZVPtNbuOEM2Xy5PT2TwNOKo4PhWVBNRH95RTVAeWYw1f5bRl88yqsuz7OrlyZcMnlTiqNCeEqM+DXmdsLXJktGXb9YtU958ZeVJJY6OPCmxPjotuV7OKkhE/kC+FBcUtPLlO/H61XutfmtuQWO/4tvw1IWfL0OrPEC+FBHUuObNK3EpHSQ9BIc4chdvB/lS2EKNSz+g3KO7jCSoDeRLcUEhECgoFBQCgYJCyIPvJQAlnBMUFCID3G6v0Kt8L8uhUhQUCmrm4Z1Ahc1TnvnTar/KKutCQeUkqHGb2/AWvohiwItiJwqYeSPHnKpbUFASBAUdaBkpDZ03QAS3AUYUB95ibKJ+z/9vRAGCWp9+sdcE1stwvBk2DOEs/0KG4yAIFNRMCMpraxvYv4A1HnqNPuAUJ7R6QndCLcBJ3cluRiioXAVFNrMKwO0DsGdY1jfQYgoFpVgM1WJLZdZYc1PnpQYrr+FxlpBnmZdrsY24sEV49UoDCHLdhuynQFCir3REHN2q670QWvYLwY8b3OaYsfMTvnrxBoDsJTRoTLvhx/v7ua2ZNI28jnq3EKIgKzVqF5Zvi7OPFW7YctJk5UciBcSRv4SkArRmrpndpXq7fRJ30hGzBNjy6Zq1JUbJC8oad4UEGOs7WuYZ/raBgJdJIxDHOWbSCXmjaex5klPHOHkIhEwXEScBgUBBIRBK4v/JwORUVVGwHgAAAABJRU5ErkJggg==)
It is also known that if f(x) is an odd function then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Correct answer is C
Question 21.The value of ![](data:image/png;base64,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)
A. 2
B. ![](data:image/png;base64,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)
C. 0
D. -2
Answer:Given: ![](data:image/png;base64,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)
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)
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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASsAAABPCAYAAACztuNMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABH7SURBVHja7Z3Pb9tGFsdHaZFT6+ytP+JRL9s2vVUa6VZsLy5NO0m7PggOTQjdJqgQCIZ2EzsQCsORfXM3affaboFNk0OdGNieugvUTi67hzbJH7Bo4tybH/9Bk3j5ZjjiiCIlkiIpSnoBvkArWRRFDT967837QTY3NwkKhUJlXXgRUCgUwgqFQqEQVigUCmGFQqFQCCsUCoVCWIXXDiGHCCEvdKryAi4OFAphlSktMXLFAtRTUI6QZ4TknhGq/1jb2noJFwgKhbDKhLa2ai81Ghuvthp6QTdaf1jW6AozN07gwkChEFaZ1IbJTgCkLFitIqxQKIRVZrWssU/1RqtguYRXAVYHli+I1wWFQlhly6pqVl8vEHpHX9l412Tk24Lx2Yd1TVustlqv4QJBoRBW2bGqdHpOBtT5f0OwnS1dwcWBQiGsUCgUCmGFQqEQVigUCoWwGsqH78pc7xQuEBQKYZUVWD3tJVwgKBTCCoVCoRBWKBQKYTWWqoxgtwXrX45gpj1ec4TV5GirWXt5lpJd0XWhuF9pto5m/ZyhrU3D1Od13TyN3SFSWidbtZeM+flPdLMxT8jOIbwmCKvUtayXz0CpDfy3Ce1ipvWbWQZAs1aZMhm9XDaXF3EBD2G9mOVFyozLlVpzCq8HwmpoglYxlBTvZLUuEEBlMPoFq7aO4/c1xHVSZcctYH2BFhbCaniLsFV9jRG2m0VYQSeIJQtUVK+fj+o6Jh2Tg3hOxdVxdVxjPFBH+oa2vErIwVh+PoRVxrVWnymW9eUzmQSpwU5SOrcdxUUFYNQ1eoEQ9iApEMN7rNUrbzFKfrL++zceA6SFOwu1lWPjuFYghjVH6TYzWifx3kFYpSqwPExdP5PFeFWTbwLkb8jYWgQIWwwhT5KEFYC+VJr7XF6/1kr199ab/kxI8UG12Xx9HNfMxor+bp7O3qg1t17GewhhlRqoeEtjOxaUNdMerCrCzG8jvbZZOcpo7naOkOdhYSVcx/5xGbAytLK25ga9iAGSJ+PcfVX0QFv/EO8jhFUqoDpruUhUO3sB4iyNRmVa1xuVLLkb+nTuJqtuhA6qO3Euc12fJjfDwgoATrXllUGsLUpyj/02BLpjXP5g7J5C1P23zt+IWJnf8SpddaDi71yPB/rB2qiy4znYQW420bpCWCUrdbqNUP5hVHcrEauKWyfsdhT3jce52NIlAbz0YCUhZLBDV/0aGcLfrNQWjpUo/beMceXZB99Uas0jXW5wrTK1qLPzeUIewt/mCH1Ei4t/U/8W/kYv5b/mx6LFn4y68T5jZqvrmrSqrxUJuScsTc7z57BpITZXyH34f74GGq1CoGvMX0dvz9TXiggUhFVqOhAZyn1/5UfBBQT3r0RL3wGc0oQVQKpWWyhZhL1LmPa9Xz6SiKPlHst8MYj/WC7jY3eeG0/ahXOnc7vycch14mPTprVb8vhLRXJNnit8Xv4jxJau+lmr8DwHlnUMGXPi15qwe0aj9WZYVxAD7QirVEF11mBLIhBNDqhWv5CFbXc5xCKsawv5WNJCTAtW/H0o+dGZwWhdR2EBTXW7ttb5uCBsuayXCCneU88RJg4RQh+7LZ2GTs+L72l51baK9iF2JL8z/hgz13udK1QuALDgdTXLMpul9HpQi8rtCvqBEYWwSsaCUW4yfoMM2R0UNz+9EeYGgpuVQ0ZfPtcFhx6w8ppMrcTyXux8rvcGBLwfWD+228bB3+3a9g+8t8/bo6pAHsN67lZjo/HqHC+Zok+0xfrJIOfouHDg+hUfFEv0epS4YPtcqH4DS58QVulYMEX6JUABym/gJsuXtK+GvfhEfKW4F8Ya4kFty5pRAWNZDUe0aXILbspKozHtlRxqD8v4TY3ftSdUu/p8Bc2gb7t2LkjCnEaAWD/XyYbJA09Y2daUPDbA0T7n54TSe8w4uxTElbfP5bnqUqbxPaEQVgNAgd6J4gJkDVZe0GnfxCR3IP6/09WKM2blFc+xgLLvBSu3xeUDq32wnty7bYq12D425HZppfxX7c9bPHWtl4UFVqhItqX/gb+P6vq3Kx/GNJ8sqEUfNWwS9LUIq7ZLQe9lDlYxuRdp7wa6jrFKqL6nfgbH4rIsPVeXC7HJIQBjx8D2wL1z77a1rS477mX9a1tRTkKqZb31cDV5kJ/q26obOVNrltJw18dJB7x6Yaaom+fmIq0RU587YX2//Vx3hJXqlvSJoQD9ldhODmHlXJeKRy1gkwetc3tq/Eyej4CDtc4t66dSqx2RLuuaUT6pxo7AUhRWD8TOnMUsdxPBJeVJqWzmourG2TlevnExe7d0W14PG6CPhKvcnA7z/YaBlXOtxqMIWlqng5apweZK2Wid7HXdM/GBvYK7aWaRB42hQF7QByz/jWWF/ZLGr+iowKrVMN7k7hot3F2o1UoQL6vZrWwgz8vzNbCD1nZP4cdZbGoQOrvbkbpg7zBC/IwtnjXtYx/RLQjKHC5pgYnWLRx8L9b5LiLzdHcBohDDEwAU0JDJwfw8prVbUNMYFFhBYQXvUV/UTlhm/J1BLdasSFin/jWrQYvbZa2lZUGzTMNKTkLO2Ul6YYK4sUBB7AQe9FpAncmE9EmKsNqJBVY8pSBYrEr9XtxWkd/x7VhRO1aWz7N/9XMLwJopKoXPsKnhleMk8qIgrUEeP/+wrBt/kdeFfz7dON1o6O+1jweJoT75UnYiMD+W7GLRHesLnhgqYdUvMdS2Ep/2W2ujIlGzmtvrVaEAP/AA5/YPkvWDJnZsu40RUQ0we9NvoyNT8Rkeg6Dp95MCC0Lm7ASzUFKC1cfHFg4ffgcCyK+gu57hmGer+so7hw/vH/u4tRDUih8HWPEfeVc8ssvqyuUedW/0kIPC4tpHbgtLzZeLHVYiGBpPj6Re29RpwSpIYh8kaSKsUJMOK7/EXvV5y+rapZq5rnbisF16UVTvsXsquvVqt7xqLQf7ksBsI+x+pdk8GsMXPtKwClJo6+3D+8fmbFjdR1iNBKzue8Gq8/uuvOAFqzgLq1OMVRVhR9dvAwNc/LK+fNonJLHn94PPXUFCH3vFrjouar8JxV7iJSp0dscObOZGGlYB3tsLVq5C26dKoe2Ue+E2azMlaNki4iP0EdPO1pwEzk7AYWb0CFkZPgH2Zr3ytv19PyWU/WyarKbCKu7C6nTvme4yqCDi91CuM/euY81bEPQKyXSQUN5sUZSzvohKvfl2VGCFgZX37qGf+m8Ri/qzaLCCQlueHe5TaKs2ZrO325/IoO45U58T+UZ2sqarQwHCarRhBekRRZLbp7pxEb5DNf9LtaziLqxOQ+I+YKEbK3L3cDp3E9a6FyskrEhx6Zr7+fhMYct8y5P8/yCpLkoOSRhYyd3DIAqymyUufDRYBSm07fqClV8UkeHt3U0TYTW6sIIb7VSRXHMHoJV1seLhHv2oFlZbx9zOYqKpV/VAOPeR/ez3ul5VC/H67tzfJM+mZxc3wzYjG6YbGBVWAQtt+XN+uU7SBfXy/RFWowsr+f27odQrwN5ZWJ2PXFidQozOuVdD3Od2N5DLvdKSOmo+XT/gsX6IA1HxvwrFr2Ev9CjCKkyhrf3aK2rwkLSvl7fvHwZWUeKNqGCKAis/KPXbDYyjsDpxWElXLQSsgA11y6rs5+n0KrGKFVTrRuFDcAXL8+afwwJnmDGrAWEVvNAW/p6S26Sk/xM2JCBhjpHcvjtrOyKsfosab0T11oCwWg0Kq7gKq7MGK/gM8LmDlOQEglXU3UCpzyxQWRf5v1F7QA0zZiXiRhHdwICFtu1fF419CotRzdr2e090A0fXDRRb8ND5oTNQ7AcxO54TS2F1irC61Q9WssjZ3QjRr0d+r9QGh/gRdwPtnkfPCWU/DZJ5PjKpCxA0VS4kmLb9Cm3bnxF2d3jbEnczO28LEGE1wjErJf4EhdGq5SQLuNWE6iiF1Y6HcRDLc87jzlr0eqxXXMnL26LFU1+61zzvv1/S/+pe2x0eSZwxKx6jMspG1OGb6gWB/KMiL7cp3BUN4tIrZA4CK1gsMPmGnyMvF2h+BF+g0h73mWj41l1oq1hwV5yi3U6JhnmdnxlhNbqwkh6A0yu+9jvIubKHWhzwpoa2+x+1sBomF8EPp9fmTJTnlLKzlV6POdaPP6x4m/CK0ybcc81r9RXfALuHizmYOQjpCnn2w6C1fF5uXZqFzEEy2L0sT+li9iu07TSfO2ulVAvV3fUBYTXasBJru3xaTuUBl190NM3/qq6PpRL5R5TCarHm8g+97pUoz1n3AX9POiPOwe8xJ3TSHf5ov87gnVt7xFG9E13bsLLuxcTyrEZZYcptoqpf358G3ylpnPeA1Q7CajRgNUnjuBo8/OEPq0HjYV5WFy62TSdRL0lY8WQ4XpbUvR0tQGYU3JnKWMjcP3yQhbq5MIXM4yLZ7TXuadQipuedyoOLftPZoUkSVtLVpcWlL6vV5lFlmMMUlN149X5KG1bi5o+ni0Y/KzNIQ7Z+krGXYWd5TyKs2t1ePcpiBhHfbYfStbi7LowfrMIPEw0jgBLL539wN6nzq/1KE1aEp1VAQDdcN9Eo77NWr7zFlKZ7OVq4AwHkCLC6lIUi30mEFf/cPD2juB/XoIx2Mz9z3bOTA8Jq0780YujnlSKsRKoF7NwkCytwh0uluc/VHkeiuLf4YFSnw0wqrOROeFyuoGjmN7vrl7uFsFJh5QpwTwqsIMcH2pi0m6KFhJVwH/tXCvD2x2Vtza+OMuzkaYRVBrwSiF1RfXvQ0iCwqvoVbiOsNp3t0qzdLGnACvJhIPZDdXM9ylAJ0KAju+xJNI/dW+lOAF3EtFQg+k0aUhMeO2NjyU2TmWRYSWAxZlyMmhvJa2T18pl+6UoTCyg1Mzerc982/nTsj0l3CuW1aGzpUtQJOIPASsLEYIeuuhNoIVHSTqAUwx/qxvuMmS35OkiwdE8a4k0QNbZCKfkFctYapj4PAyQghw2SbtXeYgnA6v6kwkoCa5C5gUHK9CYWVjAuXmaOV5vVo3q+9HXWxn8nPZbcLvH4Do6fNqwqfCd0oWT5f3cJ0753uxFQ1iSPKZvTyd1aPhXHY9KQ3cAOxt0f5Ev61/Lmkakp/UatZfV7Qk0wrJy6LZn6n3sWpOB5nGBl9xb6Qv6ipQkrZzSYrC0VPxoSWOqUE+ni8ceUYli/glev/mDKBspqcuuJ7SKsEFaJCHxkUQYBpTGDTZNNSkm5p3YfrRUV0EFh5dWeB2rYRF2bu0C7dwwD3hPKT+xyFKgVuyAfl10HxIw572N59cPvBauk8uhEwi+WRSGsJlxQgxW3+8JvLl447cAFiq95L3le5Q+F5N7Jod01a+3OG8+i1nfKbGgVlKKGzp4zR+k9USTeGSTPCqz4eyaco4dCWGVePGE15pvMCzjOAEp7eEWI6c2D7gZKKLt7ekMOlj3pWZwbb6viWFhZgRWcx6imXSCsRu0idDYezGUKVjyPZfZG2J72kVzOIaUu2MdYVYcrWP8OqdCSU2FUKGQBVs1m9fUCobezONgBYTWGguxtGb/KWuW8jN8ktZOVJqycvKfOWkBIOYAyC7XljsZmLqo7hHYuVkfiqGyEqH5nbVgp1ytJWIms67ldjFchrBKXqEfK34BdMb6rk9f+nrQVE9q6qrLjh5hxNUmrLw1YtRrGm7xXES3cXajVSnajwimT0cuQ69VxLpTsUWZetofnvljngzUYd009GyHu7BwCEPLxVzxYLxrZwYYAtNyWTewsAB6J0yKHHLE0e68hrCZY/JdRCY4mEdCOx7qi171GascKK55OEDxW1YaVTs8FSf3gFpOIQXUUcruTCfm56MbpRkN/rygLniEx1C74Vhohto9DNXPdTodwHtPr57vicz7DOaJa5IN2yUUhrCJbBXHEXxKBqmVd8e3xhLKwUSHhzi1yeh2tKoQVwspD0BLlDevc0uxPj+qWmFJkrRPFdUUhrBIXbyesZDbDrlTWui+o7hEAC9xUBNbwQMWHpFigQvcPYZWq1OC1EzDN5thuFVhls3EqiwMwx/pmgcC+WT6FoEJYDe3mn6N0G4ZJwjiwUQmY8lbIunkab5r01okxP/9J1M4CKIRVPNZVe3cp/zDqRGkUCoWwQqFQKIQVCoVCWKFQKBTCCoVCTZb+D2GppU4xVXsKAAAAAElFTkSuQmCC)
Adding (1) and (2), we get
![](data:image/png;base64,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)
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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Correct answer is (c)
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
as,
Adding (1) and (2), we get
Question 2.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
let,
as,
Adding (1) and (2), we get
Question 3.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Question 4.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Question 5.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we can see that (x+2) ≤ 0 on [-5, -2] and (x+2) ≥ 0 on [-2,5]
Question 6.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we can see that (x-5)≤0 on [2,5] and (x+2)≥0 on [5,8]
⇒ I = 9
Question 7.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Question 8.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Question 9.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Question 10.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Question 11.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we can see f(x) = sin2x and f(-x) = sin2(-x) = (sin (-x))2 = (-sin x)2 = sin2x.
i.e. f(x) = f(-x)
so, sin2x is an even function.
It is also known that if f(x) is an even function then,
Question 12.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
⇒ I = π
Question 13.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we can see f(x) = sin7x and f(-x) = sin7(-x) = (sin (-x))7 = (-sin x)7 = -sin7x.
i.e. f(x) = -f(-x)
so, sin2x is an odd function.
It is also known that if f(x) is an odd function then,
Question 14.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we see, f(x)=cos5x and f(2π –x) = cos5(2π –x) = cos5x = f(x)
Question 15.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Question 16.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Here, if f(x) = log (sin x) and f(π – x)=log ( sin (π –x))= log (sin x ) = f(x)
Adding (1) and (2), we get
Let 2x = t ⇒ 2dx = dt
When x = 0, t = 0 and when x = π /2, t = π
Question 17.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
Adding (1) and (2), we get
Question 18.
By using the properties of definite integrals, evaluate the integrals
Answer:
Given:
As we can see that (x-1)≤0 when 0≤x≤1 and (x-1)≥0 when 1≤x≤4
Question 19.
Show that if f and g are defined as
and
Answer:
Given:
Adding (1) and (2), we get
Question 20.
The value of
A. 0
B. 2
C.
D. 1
Answer:
Given:
It is also known that if f(x) is an even function then,
It is also known that if f(x) is an odd function then,
Correct answer is C
Question 21.
The value of
A. 2
B.
C. 0
D. -2
Answer:
Given:
Adding (1) and (2), we get
Correct answer is (c)
Miscellaneous Exercise
Question 1.
Answer:Given: ![](data:image/png;base64,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)
Let![](data:image/png;base64,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)
Using partial differentiation:
let![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ 1 = A – Ax2 + Bx – Bx2 + Cx + Cx2
⇒ 1 = A + (B+C)x + (-A-B+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) A = 1
(b) B+C = 0 ⇒ B = -C
(c) -A –B +C =0
⇒ -1 – (-C) +C = 0
⇒ 2C = 1 ⇒ C = 1/2
So, B = -1/2
Put these values in equation (1)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOEAAAAtCAMAAABvR/yHAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOgBmOjoAOjpmOjqQOmZmOma2OpDbZgAAZgA6ZgBmZjoAZjpmZmaQZma2ZpDbZrbbZrb/kDoAkDo6kLb/kNv/tmYAtmY6tpC2ttv/tv//25A625Bm27Zm27aQ29u229vb2/+22//b2////7Zm/7aQ/9uQ/9u2/9vb//+2///bBAdnmAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADR0lEQVRoQ+1Z63raMAx1WFnZrd3a0a10DWWB3cLSJe//cLPlC8SJZBkSt9+Gf1BojnV0LFu2FSFO7clH4Ifx4E8ZdCUCGrSVDrD8LJrNq69CPH6UH2SLgKbzP8hUXIrm4fuVEle9paMYAQ3SpgNoVTUoFFIC0SKg6fwPM+Ugyig0f5BeEdAwbzKE0VTpGIr8FmeOgCZzn0G0napJmmdZdg7TFD77WwSUQZwM4kmick0ENJn7DCK9tlyr1K5BLkMWlEGcCtIs2guv/nCPUUdAud43S2JRMIxw+ke4HQFlOKcg63fXRymk+tfvZWqR7Va7rX8o0mAMWVCmQjqxcYxQidH0jwhMBJTjHGAYHpK2GP2bRTvTkDFkQ5+TQvG0uZQRg2Nj6M8Tvav3N88dCsoMYpO/DF/YCFus/rABNndZdhY8ekdAeQoLlbbIsz5th9e/uZMbYH21qq8VFfxCN0Q+lKdwYJSfCq35rd6Sarj9tg5tnR44dGBfDzOHKdRhq+awIJb7Iez0wKHGperN6jDnBumFKYS4bW/K6pN/Ae72QKFuQkyIWT6IDCrveCfQHfRx/lMdcS7FRorcaz1j0g+1JySVOMaTqG54uiEcaAzxzIKOCTGQxcQc5Z0/x39B6IxheNqRT7H29kA6dLmdwrHnZNf+iDH8n2bpdrxlGJ4TI8bQkT/T3WLYTNNj7dsc2yXXN0cdSz2uFDHsHSyqymzOUKnGIDzTD0FoEVhFBeTDB4IIvWigXOKUcfb3/wOrRuD+rqLiTSV1XwERaM2FftFACURJ+ztFV402s8l9NZv+MscGe7nUCs3DEi4zRkP7+ukQeH3TQVCZCCmGRzxAzcsbcnFR2pi1yYR+KOfmwhTDOjUbh8AvdBbCVOhIeQqDcOnyC3nObSl0JT7zsKuwF4ErUAxEg2HtmiQV8uFyab2WJREkhvohXLl9hOW3COJ0bCDcGFpSZgxDcPH7S7M4W5lV5ioqRo95KOQqM//xay4WQZQdLATzGCNF8JgHmPn17LzJs2kJmWJXUdF67EPQr3cMr2bjEHimcRDEBZS0H496ENwjiwscAhsF9TYo9Fo6yJ4EEDyxBMcgiZujkgTHYFT2k/HTCPwLI/AXJ8Fpw3+YqJwAAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYIAAAAkCAMAAACzFs38AAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZmaQZma2ZpDbZrbbZrb/kDoAkDo6kGYAkLbbkLb/kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22//b2////7Zm/7aQ/9uQ/9u2//+2///bG8mEMgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEOUlEQVRoQ+2Za3eUMBCGYdVavFXX1Xpt0VraZetlEeH//zNzAQJkJplZwtmeU/jg8TTJk3fm3UkCiaLlWTKwZCBYBuqb02AsDMSfwzfC1+4IyTfU1x48W7vX57NbwJ/DN8LX7kiTb6ivPbgDApjPbsEhc/hU+dodmfIN9bXTTNgl8SWt5yHpIZJ7IvhRDUYA4fCJneoZ0SYzxemf9OgW9EXwE9YfAYXDJ4IWBEZ3c9T0/M+3EA1E8BPWGwGGwydCFoRGd3OUz66Ja4XoVmdP9/TeURETl7i+iMEcJEJ/BBQOrHo+NIncS2OxoluQx+J5y/KAtsT1RIzmKPwmDkYA4WCq50MTyP0k5o+2jJwyu5YJzQJcBJXQCmOEA6Id6zIdzRSd3QcLcBHMaCJGOFwL6GiH6PLlrfUzpoO5FXAex2eiCrI4PtmLxcBVD7CIkkFoxRHDQdGOKqChfaLtlbJOZ6qCMrmI6u8y8ZnYbdznLlgEh9A6QAwHR+NCaWiEXG3kNqqf8eZLAzMLQHbPTsTZSe1LdSqqoNvERVFYUmARGMElhhgOjp5qAUF0vhouCEazsWny/0SSqo1Mul4Uy+Rs7TSxl7hmbgdh7KEZIU/NpqiRKKQQRJz16+CjKWHjFhzwS3cM6WuJcs/BF/ztsgi8hciBnlgFGPkYC1FfS/Xxk9lwyAsRSpi+EDnQAS0YhN2JhrZjuWaHf+pUflPVe8G362rj/MIqdwtLAotgqoASjgPtsoCA9ooGDqV6zAxPvrqK/n0QFtSZ2BUK50s1LIJDMBaQwsHRLgso6ANE16n9weHnZ/v1Qce4+0IumfomXq1/JfFFKk5hcil0fNiARIjqYRCMBaTvJzjaZQEFfYDoamO9MpkDpF0c5SvlQRCTDB0QcWBdhiNZAmZD218WdZaxS1Hlj/oH6dGYxEoh62utRf4tXqLbQ++ANP1id0Z0E0b1fmt/Slf5NZeio8osn28jlWX02tRVRJAxoAiGg9W7q+hOnXpHJDQGMpyAJrOQjmUSv+kW97tkdV0mJ+0VWuuNtqBp3MvjjS6C8SVm10OaxHkGIsxEHESkf/xDUk/hKIaQaM3qgmeh7c6F+I6w3re/+qEFkW6Ur5+X4x4NqeshTJrwtBgWAqk8JIaQ6FHwLDTQOX/8VeXY/MbblzrxJ9VoWwD2mCSkmYjDuEO+fygLbIX3BA3J2L0QLx9IFUSqUb1nIVXQ9WBdRts6mokYecqxL1CjKmgVhkS3LL5qSMXfH3X65LZZ6bv71ibhTWMkVvrmL+Mb2baH3C0mPC2GjiiEAwV0G4HFEBLdsPiqwRpITutM3K6o7dTct+qE75pGZZA+mI7ukbse3O14qKXDkPOkFxrAAjSGkGjN4qt2a0DrWgxT51F3krmHUnJCHlJH77uv16SHlK0jxeo16Ui6lmmXDCwZWDKwZADJwH+xD7PPpd16kQAAAABJRU5ErkJggg==)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 2.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
let![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGoAAAAjCAMAAABLqG8BAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjqQOmZmOma2OpDbZgAAZgA6ZjoAZma2ZpDbZrbbZrb/kDoAkGY6kGaQkJCQkLb/kNv/tmYAtmY6tmZmtpA6tpBmttv/tv//25A625Bm27Zm27a22/+22////7Zm/7aQ/9uQ/9u2//+2///b7Ag+QgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABfklEQVRIS+1W13KDMBCUcMAmnVRSLBIc4QRC0P9/XdRMkSmn0Qx+4Z6s4WZ3tVdkhJYYcIAlm5m8ya7v56JCiC5UbmWdz0BG1jlQK4sxdigsxTxugVxV5MAE5NBpLF6o7BwzslsGElFjGd7WCXNoX47UqqZ2/aG4T9MWpzTQtmByoPtCAQFGeAKhEfTxNSYOspjGERr06sHWBjMfjFA8HlFRuwXbg9CvPuuZRmK19joILH7u8LTO7LX9nOgPVlQCYR962zIMOJRG+HvRb4c6s5R7V/JSHSWSdYK9rrpeS2oEVAQ5vRGiFXQVPaFEMOvzd8oPhfhiJCKy2iG6mm6XBgHRM667itTQSJUctDkLBapRjURhYHk+TSU1K4TsQl7iYOD+EuPWrThD8KNa3UgEU9UIv+8s9nc1VcFXP/WFhkNbVHdvstWNRESCnH0CDOSWKYQs3DAir6FrFWM/lSNTdyCVD4+ZiAi/vg97khQCIMor6D+nITB3BIDMJWXKgX+odyWZKIFDdwAAAABJRU5ErkJggg==)
Multiply and divide by,![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 3.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
let![](data:image/png;base64,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)
put![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 4.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAArCAMAAAD/hH51AAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgBmOjoAOjo6OjqQOmZmOmaQOma2OpDbZgAAZgBmZjoAZjpmZjqQZmaQZma2ZpDbZrb/kDoAkDo6kGY6kLb/kNv/tmYAtmY6tmZmvJA6ttv/tv/btv//25A625Bm27Zm27aQ2////7Zm/7aQ/9uQ//+2///b6+3zKQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABV0lEQVRIS+2VXVfDIAyGwbq6+rlqtdNOV3WOOirw/3+dhK+xHeZ6TrzoxXLXQJ7whtAQMnJT71PUCbvbCgcghJ0Aqr3gmGtgVFuJIZxiB1UA6oyxQUnGukm9UjpZI04nH1ayekEAdOjmBvVS5D29wwDkE1cN5qXJCllEXPn+I9o+AE9SiwOC2oFlMl3h927qlQd31ylAN09dn3x0fcm2MX0ZfQDUzTqR6CBRO2q0KGvOyg/gqsY0bZh1lgv6vouzpShy3s+5eDYHhzXn/YQyZREgzDpxqb1WX59zNuO6Ld0P3OayXkJEQU1qd4IAUIsl8frYuc3szG2NvYauDVBu2updVh/ousrjmnq1SW8MMFMnI+TnTTWTcG199mUk7Hq3EvysAwlWX1dMVUvDGfpsDUXc8wZAmHWmiAfsr7UQstceuyg2O/pUUo0UBUWtnEalW/lo2pFu+AVxcCJocpuwUAAAAABJRU5ErkJggg==)
let ![](data:image/png;base64,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)
Multiply and divide by x-3, we get
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGQAAABBCAMAAAAQXfHjAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6OjoAOjo6OjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZmYAZpDbZra2ZrbbZrb/kDoAkDo6kGY6kGaQkLbbkNv/tmYAtmY6tmZmtpBmttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///bNE1fywAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACnUlEQVRYR+1YDVPbMAx1ClvoNhiFwrY2hTVsJVBoGv//HzfZTlzLtRLla9xu+I6jd5H1JFmW/CTE++JE4GkaTb5zBHvIyNVP8TxZ99DA3JqfjQ+yv1swrekulkan44MIsY2X3W3k7Cyu1iIfG0Q8xeOnMMdbV2Z8r4WQq+nw5yd/f350HckWSTNIdr5pEyCZfH115XcXshZkO9fXOv+kLSlmkV5L8y8KI8vkEn0obh5lsri3uB7i/jo6MX63qSG7ck+FlGmDPhAg+fkmqzZkB6GGyMnko5JIlV7Qr0OAjD+KnQU5coXMyupDClW60vcSO97RIH6g6azclS1AJuAJPh0TAxpEpDoIdtFZWYFA3fly4YcWglgupxvZcIkUHUpNVh62ZOG2VueJC+JnJboVleri5puXZ83hckH8rAyByNW6mOEYN4N48uQlLrNLpnDouyhw8sfhsr7PPHGUla4n5p7IJJqAJ1EABYPIuxhS4VQ/fVpcef/GN1xeN2XZNx6cCN0OBlQLR1SocBVm6NfBMlWYu/x+wtrXsp+wdP6fQsGKN3oobJkd6sfoFpcAbxOugbz7Z9+cvv+sN2fPoDW9OXuq19vruvsQ+rWOuu4+GAgoqn+iD4REdvfO+v/qfONBtcbiFpGbzpYHNur+XsyX8Ndp0KFypWkOU843ivkPwOmyMmKb5W2KzJTzjTy+BIhaIhc2gQJB0ma+0cMTMOyIQ7gIdr6hzkOdC3chNueOSPAHo66ab/xSZ26yi1fqXTaHHpXoA2Uzc7xg2RxQCGQXSfNcQG6pr9icfIAMdmdjIZrnecQv9QSbgyLbdGv4pZ5ic9AtwjTv4A271NNsjqJ5KGSsUh9gc4ZB0jQPgXBKfYjNaZAamse9gu9ybx+BP+YYRXw3Y2KbAAAAAElFTkSuQmCC)
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![](data:image/png;base64,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)
Question 5.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
or we can write it as,![](data:image/png;base64,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)
Let x = t6⇒ dx = 6t5dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
After division we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 6.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using partial differentiation:
let![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAX0AAAAyCAMAAACH3vtuAAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLaQkLbbkNv/tmYAtmY6tpA6tpBmttv/tv/btv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///bOqQQQwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAF+klEQVR4Xu1ba3fUNhC1lzy2hQa6FPqiS2lqAq1LmnVq//9/Vo0etkbS6GV52T2xP4QcosedO6ORNL6uqvVZGVgZOE8G/n1T1y/PE/o5oh4+vfh7wt2/vq2+bP4MGdLefA41mft3jMs72kJo/gnSMNfGati/ejAG6b4JT9t9+5tv6gTq9GE0Gh246AkDaJJJ6rY1e8JBmDyw6DDsrwTnw/57a4jW/i/V5p7lpUse9l4XceqGPZhQb16a3nVghnE3Nw/VSKMLl6vfWxEoMQGTQFW39cZWwkjOpgfl2MMzLe2Ipl/0tD/sdRzt5rYaGtGllf6TTtSbSer63TVz713NflqPMW796mG4g1hTNDpwiWDR53l8Uyv4CM1cdqqF2W9+3vIAH/YWNS3ac5G5/Q46iZ843DArkjoxeL/T3aSIQR26LTQc3kMcCxoduGwvdzefW8V+2eAf2W/q+uqhreuiS6H/4S+ReuQ02iQHRv5hmsxgCf4gsxbKDaiZok6xf13ZRqAOrZZhBY02LuE27GXmK8V+ZKaKXBVT7DcMmjlp5CBks/Za4j5Iu8dJ+h3kaoJ9EfVqz2i0ZeNwkgzg/36/ZInKMkLvMOy19CdotHBJU0j2Kx3NXHqY859v60sIAzDWsw/mzAQ2CPcqK8lJsLnNMxYJd2wxwqyNllFQs2lQ8OQVbNLW+HoHnJs4jRQuD/uu/JZDDl9i799Vj3semd32u8LXn+4FnEjAyilvOiZh+UI+KjMMH9iR5w/YTDX2rWYTdbDrQthjI8wOBvtAowuXDUdrh2Ihl3TcrxNbo54WiwzMthH2wHJXRJGTOHKeREXHvqIO7bqGEWTmEcNSuI4U+5xlfmSr+h9/so+Fc7zQv4ZoPEB2H62kJnGwr3gk8z6KfbbIAL05PhpXLA/5YPaNfkfK+w1EPY8ydhATXij2HHiK5IOqzZ2cxGZfgZEHT4GKyPvjidMaH3eo+W7OT5xi+6RwkewjNLOZgnB4hKgZwA8HDq/QIw+E/Q5GF+d9ehKL/futvLuiE7bzzCNuWw3Dbo9vHFE379huzleAOle5cVnsq1VT9rz/+JZlZlbKYtf1DYv9uhz9MBgLfviH0c8vRp5JDHPZUexWBgF911UuFZWGC0asbQQed/jICisXv/AbiCgyEbiw0z5AOebiV2hf9q5bKM6Dw2TfUnzBRpQJgmA0GhNxlQ39KKBFGiXVEqcZvVXFROp0O0Yak3CVrnEWYTZqkKxicKCinkQdIn8qXCfgWqi+H0XfKTZKoE6Hv9J4is5MxtQ9X/zdWzKmJ9Rhuiw/IaO/sqmiQiuexd4Lptjoqk2l9D/btu1G1sknhxz1N4K4o2I46mTI4JH9s42fcwO+Zp7T8Ni6635FP5gnzoT7xyneORLgV6eHP+nurZUtDKujVJYLWJ8Ef9JEsfIp0ilGwS/vvci6070pzTKs9qssR6FZ8aJTJPwqgD8gEl0Mf6Y0y2W1Xkw1VDGj0Kx0wZUqGeMqvS0tc+An4bPX1wvhz5VmuazW1SVYl6EJzcq+bKDg4xeKDmmZAz8FX77Ukm8Ii+LPlGZJq5ESjFRZijmk1Kls8FPwQ9IyB35aJLoc/kxplnq3rCnBaJUlEprFJuq4QyEFn2Yfvxuf8AdFoi6ZYhxIulWmNMvu5lNZYqFZSRUEqXgLyGusfj741WL4M6VZ44VNydl0laVVPnMKzebGDe/vVLxFSMtM/F741WL4M6VZo9WUnM1W27iEZrM9QCreArEfwh8plJuLn5KMBaRZGUqzUWhWUlRK4piJ3yeUK4g/U5o15k1KzmbBH1VvhQXVolTuV6TpKUocAUL4aaFcUUE4JRkLSLOk0+KVZqPQrKywjlS8zcRPC+XK4s+TZgmro5VmmtCs7HmfVLwFpGUh/LRQriz+xPN34Nux8DZU9K7o/rLRB+L08FufxdLwU7+btEYqGzp8/SXAT/7u8wj4UanVG7253wyPgxavcZqVYv/iO0X84XThapHyVkP1X6C+nwceFk180I1znBL+bMPXjisDKwNPhYH/ASg1/v1fYE17AAAAAElFTkSuQmCC)
⇒5x=A(x2+9)+(Bx+C)(x+1)
⇒ 5x = Ax2 +9A+ Bx2 +Bx+ Cx + C
⇒ 5x = 9A + C + (B+C)x + (A+B)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) 9A + C = 0 ⇒ C = -9A
(b) B+C = 5 ⇒ B = 5-C ⇒ B = 5-(-9A) ⇒ B = 5 + 9A
( c) A + B =0 ⇒ A = -B ⇒ A = -(5 + 9A) ⇒ 10A = -5 ⇒ A = -1/2
and C = 9/2 and B = 1/2
Put these values in equation (1)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Put x2 = t ⇒ 2xdx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put the value in equ. (2)
![](data:image/png;base64,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)
Question 7.Integrate the function: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFkAAAA7CAYAAAAQNyb+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOKSURBVHja7Zo9UuMwFMd1AA6wzOTRcYCgpKTbMR6GA5B4Ui1DxWhmh3rHSZeGC9DRwQm2od2GG6TgBrnDLs/Os2VHsux8+Gtf8QocZMs/Pf/1JP3FYrEQHMcNhsCQGTIHQ2bIWzGV8CQErH0VDhkyQ2a5YMgMmaPTkJfL+5MrefYshPgr4OJjpmaXUgYh/R6qyTn+DgJWpMnYJvDHPwHESgbzGxX41xcgPvAeIKdP98vlSf45YTg7lUJ8Rs/ZBHgPj9nr9et+TZOaeMGXJXj4t5DTlxiwPzQBiP5nA+pMXj37gbrG6w8ePOI1BG8b0KTtwH+nwZgH8kYI+TlR4XnvMpmySIcSXdMyGcH4A/GezzITUBwUEGJNg2YDHd8vbhv9DfDWVOVSi1QkADfZaMv2KpDpS3ANLmbvaASvtszvjVyoYHyb6CTAahyo22NDTiUiKxu9ri5ocktg5yAdC/JgMPhDE+B/U8IhbKoSdHgHlwv8P/Df1Fx9M+l97zTZk94v/XMlUMeCjHo8gtHrLAxPM22+9Jmu9XLi02vbGF76wnoduw0++6m7dDZ5Xk4eaMCwXd1lXD2Q/eCHUt8vSSZwQUIvmmaZtoDwg5BKMH1RkYCiMIDW62sCvdWuZungZS9DZsgcDJkhM2QOhsyQORyQswU7x67BmcxywZA5GDJDZsgcLYV8SIOg8uSd9NRdV6Bhf02Hwa2ETH4ImyOorZHYHEqegjfaWRyoJk+R9+9/6oRqJeToSKhhP8ShMtqVKI10zmTd6mqQx67oFNw4OkUOzAjSni7M/Gl1Hn6TrszM+2+ehwe71oQp4c0z6ozNgUk33ceF6Zo0mnRlpr699DmBD6HLReqaBJ2fcd6Bme1MdRdmkpUFE0ZTrkwTMPJ5FGVqnBR2yRBWeAUOzPTG1R0/XXFlIgs0SpInxA3ZLmPbhXYJB2YdkPUsqlKFbBtZ7GEDR3BxLsGFx8Eh6xObzYFZJ+S6XZn5RVZ5uagIWYdtcmDuBbmEJiftanZlmhLgKJpcxoG5D+Qys3FTrkwTUBfkytVFGQdmvp7dxYUZ39OcmU26MvODiV/yCOA3SaZSk2H+2cSidJ3scmBmO7K7C7OoY027MnGii98P1rgzmCYUrE1FwE4rPt676MneRdVdrLZG2UTp1L5smzI42qb9qn5av5+sF/9dOxmp0t9ObzN2JRgCQ2bIHAy5PfEPUnkX6JRWRnwAAAAASUVORK5CYII=)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let x – a = t ⇒ x = t + a ⇒ dx = dt
![](data:image/png;base64,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)
As,{ sin (A+B) = sin A cos B + cos A sin B}
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Question 8.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAYCAMAAAClZq98AAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OmY6Oma2OpDbZgAAZgA6ZjoAZjpmZmYAZrb/kDoAkDo6kLbbkNv/tmYAtv//25A627Zm29u22////7Zm/9uQ//+2///bORlKUAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAiElEQVQ4T92RQRaCMAxEMyiigkKVWrQ09z8m43uyQW1YuXA2XeR3MklEfqP7CTgYrVJzlaHo7UBjtQIKR9tosCLRInxjPLB9BKATiWQi3w/yHEgda6kG9YT48aV5WHV0MvOOu/2avMsNvreTdG43N2M9eulTXeYh9QwdkU2uDgWdkKfsW/0XMQFydgVfBMbdLAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAuCAMAAACmok+8AAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bGD3PyAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABPUlEQVRIS9VVXVPCQAxMToQTQcEvOEoPtdDSNv//95layxRHK71lxiFPfWj2dpNNQnQZsR2zeQGpympNOxODKJqe3+AgRbSAiXge4CBEqV2GUPHMwyxhXlI5jykPAyGvDRFXEdja4BaLUyb3ISLaObm9naIYRMkZHFY+Pl29g1RkFZezEQYiXou6Z6iy4tgoE8ZQMB3/k50+MJtJ1vPxehiaSPguk9feljoCyW1lA/UDwiTU1m0m4lqu1vXxFX+ra4OUs2FHSQ+gzUet+ftj3SAddTq7nM8FGBJHLa5nFGyxOLMg1GwkG8s8eP61R7IbM1+HaT7UyZs1FS6wcg2Kr8Yi0fsFh4e3NRXR5A3kUS3Z3uvmhzdTi8uBz0bNK7fg7anS91iLdSxiNVvX1jmhcUWkYzHtewxOAL6EXz4AB20XemeRj3AAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Question 9.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put sin x = t ⇒ cos x dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 10.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAAAuCAMAAACoJ/OWAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmY6OmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNvbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bgCZySgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADcElEQVRoQ+1ZbWOaMBBO2LRs7arMvbW4dWLXUh2v///H7S4hIdgkBGJxbr0PaEuey5PjcjkeCXm1fy0C5YrS68xjVd4Oxs5dx0tSRsuxcEK8HYyeuopuCUkuRuOJt4MBU+cUyEqr40VWIv2x5u1gwMRd6gRTdeGb614OBnDvDK1WN5CuPgnj68CBebmmNFhkOYWEwctTSBeEFGFDPaF0nqV4U2sFPJwA7uHn1QMMadxJBz14B4LGIXU8z+rv8wzmQgbh5YakyHMXNsUxCTYQfxNzWCFuCVxpGb95hJGNO+nAivdhDpUAKmBxJakz/mpRRDKpqUomsGY0Votw8dKdsuEteC/qZEsvf6GHJupAnU3fWhF+gAziDKkweBRgYiT/ZFfhTov3Y/ocvXtPZ48W6iTlPDXWpc63deNOGW3G+y9lH8KcxqhXn79AEjtQFwth7lqz4P2oY5oTTFkT9Xq9qSJDlRTlE/cDX7x0J1nZ8J7UsTasgBo7ktils03rBBI4p5jLGksp1ND7DRtQIn9WatCdMDvei3u55lWwgI9bdqki2jKtYxpA1JX/dGeDU2B2hxkOSDw7hTvJvAfvxf0k4BQCcpKJjzBpbqIOj5l69B9HoNbnoku9eNc+A2NN6HM51f0udfUvr6ZvCvqcLDRtwTc8gcHE2XEe1LGS7rHrO7+o40nIgmygftgyTZEO/XMgWd44IH/nqMv272RfeJzxpONJ7ky9PyYvP6KNOs51dgnT1pLzijpv9qB5e4LqiA3f/U/+Fv+3H0nw/o6FHZq34Cu+Im7h3Zw/hBduBH6jRjNoP7ggmF7mYPtP5s6t3gO1mXq/Ky9VH+/IblDn54TY3jjwRmnL9M6GlRZSsIzUAQfKGB7hSsPkMuMYhM5vcf2Q2qhjzjExxmxGecMIGY4wuLJRZxAWaL0yBnd3LNUPlS2jFCYQAuD2nMZST1Qp60AZI2mzSbvKFnsv1UthAnEMKawv6oysSRnLgXmO+dRVxixSmEBYpTTHZ6FQ1/Vn+JsEK7c6ZYz3HmwrKMqYTQprESrAkerhMHvU5RE9RBmbSgqzU08u5I8C7sqYRoCEgB1fCrNST1HLypetlOWkjE0lhdkkTHbcoGolpaw+ZYy3TFNIYfUP0KroW2jZtNbsW5DiXJWxpttzlsJGbtBX2P8agT/XKnqcVpGrrQAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfIAAAAvCAMAAAAvmLinAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGaQkLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2//+2///bLjHm/AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAGU0lEQVR4Xu1c22LbNgyl0qX1umTx4mXdUmdt7a5rNWezZev/f20kRVIkxQsgyE7jUA9xGgs4wAGvEk8ZK1dhoDBQGIgwsL+rqpstgR6yAwK2NG1m70kuxtmPs7ICJTsYm3S7vGX7xe1Yc8bIDsZDd5btw1tSycfZj7OyciU7GM3bYcH5Wr8Zbc/IDgDQ7Zfrb9Hb6vslqeSefX3zVUOlYKmozHVgoQL4wN6yq2yG2uV8uxdlH3uRHeSB2+Uv1szjxs9285ZU8oF985Niw4GdGHUQtkHN04G/wwteTMVz6lxOcpBLQUwd1uXGf3j3rV3efxwmAGwIAfvmx5WcMBxYIGouF/39EFahQh0Q7jvc3fPkKAM71UE2+N2r+KjO6kpcr0eXPGRfS3cp2ChqNhl1Q8BBhzrptX+oqov5dlfxgV38+GdWzcVyV5V8LYjjkUTG+IYPBhf8O/F5LWY75c44yNiPT0U3yHD8sjuK5YgfvtvLo+GH7GWHc2E3Lmvaagjr5omBnb6bt8vX2/ZP3pLk5qCZXa14D+G/bWZqk7a+WHXshS7RMsSULz+XvNsZd8ZB0n58xfUeLBY/Y//OxDDgwzupJMIP2MshXe2hNKzHmrYawDqJomC9+YvAmJk9xE6suTYll3W3J0mRXB3bra3VqCPX9iL9g3ZnQkvaExLY8abILwOoyPfj9+GdkiPDF1l6sBFU2fQnYo2ybwrz+7m6+lt80wcvWeyvZvYzH+nFxUdJdXV0d3ybT/kv7S5kTyjw0FRxbwBj8ffhD+LHhi9aiAd7AtZ0u5yQvc3b6pKPgNHgWa0KPMR0OeumOeXOujluT8mi1qu3XPwuvN3LseEL8j3YE7B2hJIz9jjjtYoGf3j3e2xtHOgmvIrSXX8l7Ckl191NA8bi9+DjJdfJxMO3e7mCPQFrk5dcTONMeI0F3z6sDovIbk0vX8XM1TUa485UM2U/Qclz8fvwdsmx4VtzuYY9AWuTz+Vy9Xgn1iVinS5/OMu3ds0n6F0VWb/VFd/L/bWSN+xF3Y07Xc20PaHmaumciX8A7yzfcOF3K8XuZY2GPT5r3sqKwJg23T90u7GGf7yXPw6Lqq9wu6wueC+3/uJi8l385Scxg3NL8axNuzMVz9iPz0B10XT8w/Dd/SYqfHtfrmBPwNr0+/LxnD+1ZfLp2zGCyz99Ox7qMTw/P5/TP6NIcxB8xn502kontyl236Qdm/zwm7SToR4b6Jn4T74vnzgH4Pvy46FO7Lm4O0MGmitzqOMMsysphRiwHlYVgs6ZAbGj9l6FfD/pDt7SfD+hnUkktTjKIK6+FTzVbxFGnyqcc8J1qDUlP5MmXNIIMlAG9hfcMMry7aUVv2zSXlrFp833P3HGHeUSb2G7p1lzTxQHeFu8hZUs3hhq8fhbd3otdLWPvKSX9vfeAf1fP7FN9HBUyOMBaUHF82LAwVPBcWjdEQVzIY25HdCCS1ES5/7X/NzDfmHf4ClZOBD+BQ/GAooHlJ4IQuHwUPDUMAdH80qOC1WHkIdrbr6aU3uBwOXJG3mYPX5FD+xGTfAWtquwNaLkFHi8Ld7CShZvDLJIlVyiy7YeVYJs5uIeXwqSEmFIi5x0BYnnSSqI8FjwBBwk2TTcgClocolemhJ0yXLa0hNfk1HLivtSkJQIQ1mkpStR5UkYT2mQzOgWV84wADwWPJEtAK2X9US49ZgCczu+5DKQmBJkxyu+E+O+q8lIaD+0RVq6gsTzSk6Ex4LH4UDJ5uA8pojJiYZgDeyhtxvqkFFYydI90lMHPbWSJSld6S0s7UigPWLw/LAT0pMg/CBtDHgqWxhaRGUTYQqbXKivp+dyIzPOKUFsJQtW+xEKC4MnR5l+jUmHR4GD4JI6nRycbQxCS8iKvF4eoH79Zqv/CleyTCNdgeMlS56XnoRaHAIckm1Op5OEc4whaCwDl+zl8vTu7raXnoA0GVjtx5DznPKE/5c/rnKGIj3x4ZHggGyTOp0cnGsMQBuQ4yeYGnK6I/pcpQJWsnQKJpz2I9DLwHjaliA9GcCDwZVcK5ttWqcDVdlA0WTB+NY6smJvP3BtSfXDH5Gv1cKGS46gShYVF0r7EQAH4wVLzmjwYHCt0MvAZXQ+UJUNEI0vazpZUXyTVr4pDBQGCgOFgcJAYeA5MPA/PPSJu+9eDHMAAAAASUVORK5CYII=)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 11.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG4AAAAkCAMAAABfRv/DAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjqQOmZmOmaQOma2OpC8OpDbZgAAZjoAZmaQZma2ZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kLb/kNv/tmYAtmY6tmaQtpA6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/7aQ/9uQ/9u2//+2///bfj8KPAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABiElEQVRYR+2V23KCMBCGN1gU7NEW2qppS2yrwRYF8/7v1l0SxqElkarDFbnJkOTbf/fPAYC+/XZALYIOTUlv4y7lAGQvd77t7dZMJUbZ+XI/FEkybA+HVvXzvQOnOECHrLt2SqY92zuADnw9Li0+pE+u1/kvJ5n+Fbs46XiA8xu7XhMnzJ/fztVnFJ/XKrXn0shVclBy6pWx4QqKmLE7TDsNGZvSxDr0kjwc4lAlV+BKIvLL1X84MVowjxImTvEgw566IgogH89B3pflbIaZnJBvRm4XzWBRyr8kNNiWE4MlyAFmSFw+RhaVqcNBxb3nzMSXF1OAXaSfOO0npmDk23NkZrmawtYwCvYdezO9WekVfe/NXF+j7Y1yTq4mt4uCTL1n1BU8oPQV12Zu3xT36TqYYjdeAtI3pmDVbTmBIT8qMyGPmY+VYsdwp7Z4UvwVHZU0DJTYV4O2cuZ/0iXSR6U1J9AUUjBcw3XWAW3NcRGO5OTErua85kdy53vEqrzdj5/DzH7K4sAPy+E8H3Q6dJcAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Multiply and divide by sin (a-b), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As,{ sin (A-B) = sin A cos B - cos A sin B}
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 12.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAAlCAMAAAD2tQAMAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOgBmOjoAOjqQOmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjqQZma2ZpDbZrb/kDoAkGY6kGaQkJCQkLb/kNv/tmYAtmY6tmZmtpBmttv/tv//25A625Bm27Zm27aQ27a229uQ2/+22////7Zm/7aQ/9uQ//+2///bn9TyqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABBUlEQVQ4T81U2XLCMAyUQwxpKRQILaElUILNlTTW/39dhWM6JBzWS2bQm0frXVnWCqD9wLkQ4cavYyaZiWd+HCF2/ZyBMyMxYODMNMfk/QHfNgrSMpLH2PeOQuZqyFAE1flk1A+gXyWH7neBSZh5GXXUw6VgMXq5nhUgeNFW+cojf9b9YfiBsObjfqHbSISpSxf3x8mMU1A9h9OnC7g6Hy/JLc65AL9o6vRbfAsHJelmgGuSLKvy/untybnl8LIBLWG/pnkrKlfXcVC55bQdAspjMgPXFYsj89qgVN0tSh5dVxp8DbeY8XfVFVx2ayZqukUFto326y7WwJVbStbSaWuyHvP+AZYHFDamsVf7AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Now, let x4 = t ⇒ 4x3 dx = dt
And x3 dx = dt/4
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI0AAAAwCAMAAAAb1Ak8AAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6OgBmOjoAOjqQOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjqQZmZmZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNv/tmYAtmY6tmZmttv/tv//25A627Zm27aQ29uQ29u229v/2////7Zm/9uQ/9u2/9vb//+2///b3VgXfAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACqElEQVRYR+2Ya1fcIBCGw1qbWi8bq7Y1tWq8sK0KW/j/P64D5EbCZYhljz0txw/ryQs8DDPDQFH8b3+1BX6c3y7lf0VX95TbM7L3aH+Sd4SsEYCOroheIQk/fqBTmmZdwF+0ubpGO0UFUxp+MLGVf4TZQqKTRQXTIZv9l2ifVpCfRtaIXdoZDS/fEg0jl9iNKvLvFH1bNCt8MsxhG3v6JoUmQYvZfnldEkLefem1sp4mQ98ws66Y+RI1eJrEgRfJRYW1zZLhGUmIEZhAVPhUvIAnJX/kp+ElZDP+ARu2vMxqG03D0KGYkYafEXIENFA+EbKH2mZG3qN06SJefi3kd+XFrW0aRaWb11b5aHSlor3Yt1M9HenWatEMn5f+GkwoKlUbJPpNNtvMaRA7RVEFerrXQCJbYJtsNLJW4RH0m/ka/zyNqEyU0tVNsT1XXqzKy3uUeT3FFl3oxjq7Gxq4pq1OfpYKB355C0w6DvfGeazJb9hcjlpyQMRLi8aZicQF+lbzOhxRfY7TMCtBP0GKP4nMitE4hmjW49ToKbYas83mFUCc3hSbyMGH0Thg2OGLTeM6wuWVugyPXwH8RcHwBV84dFzi9NY6NroAsLn5IbiN9QpAvVfAYW1+jWeX9TUX+tMu4EzGnLZu3P7GsvG6jSkXlCn9Gp/LQZ1qWkejT7VR+/Ws/rlr47ujoQEf7mwT0oQiYOw3zKrRt9e62hGf2jeUloYBDPOlr3a0oAZLQy0nfnpuFF0f34ZGVCNrzg5iQ2NpklLQKBfLerJk/WLRexXmposvep2Q4DsmeUB8sWl8q/wzHAs7oOkRwbrzZAMlgI5v3XZJ47ScrPc3fdBb56vHG3S50MZgksOgxJR8NL6EfQUIlQuoGUOivBfzZDya64KVTPLPdPgN5+U8S2DyXngAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKsAAAAsCAMAAAAtg7hLAAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGaQkNv/tmYAtmY6tpA6tpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///bbZfu9wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACvElEQVRYR+2Xf3ObMAyGbdZ1Y13SJS3Luh8p2RayraXLwMHf/5tNMhhswHHt0ly5w3+QHCfLj1/LkiBkGpMCXgrsP2295p1+0mFFX92fflmfFdniLh0LK+xvYvU5ZPucSVe7Rj4Wk64+qtnnjErXYCR1i/8IKaVn3+zySwu+e2syZuHt4/2cwPLhw8rEyjcXL4sV6pxk5b/nWieRrmNgTRd33pLxmFLjqZm95tSkkWTl8VWmzs+XHFkJe39M3f2K0mChTVScFJEHKtFZiwiiGgZSVKw8vtZ2Wtzc83j9EyjYO+Wylvz1SOlVxn8ZbzOPfVjNileseas9S8VmzlGxVDzLobOyEFn4RtkMmykx48Z62MAZLbMcNcTHQ0iXGjdP3iBJ5TVBPMAU4kkuVVidNe1RNFfeObHy+Dzj30EXkX9YONuSVItcIR+cvsxPCawkef6FpdZqeGisPK4PQ0YVumtgG1YQoRrGgCki5JjXrAJYD8xSZakGbi5tGyRN1GmsRaREhxLEgYzpY7rW8FTO3NHZH/xf6QpOBH5n1CfHwks9SMA0KZE62jyJtQfi7wV9DSdpY226iJ4YrFg7d2vYGED3e7ysNtZa1+Lmc+eDzcRKMLrbw/tuYaiKI3wsK+SfbgI3xStkFownc85yqgUsXJMDVnxRC8Sj/25VeYAnsHhJ0Aw1wvWcxeNgTcy1wK3GHjbQd0EJZPBzKx6YXHouV3ljwXkAurYszPmV8B34PPtqqrE990d/1ZegrZNIu24pM9S6ZXfkYsFCr2a73Q80S2r9gAuJ1baIvnixwvnrfZZc6XifZeU5ZpBcq0nDxVW7fy3nPqV/tayezzNfVpd9DWFbfNzWpX0If8/oQ1wQ0DV9aR9KPXuGDrVp+J9Rk8FcjyVeccNjYvWrW4Mdq4sjiFm/YuCyyGQ7KdBW4D/yyErPcU+mjgAAAABJRU5ErkJggg==)
Question 13.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let ex = t ⇒ ex dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 14.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using partial differentiation:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒1 = (Ax + B)(x2 + 4)+(Cx + D)(x2 + 1)
⇒ 1 = Ax3 +4Ax+ Bx2 + 4B+ Cx3 + Cx + Dx2 + D
⇒ 1 = (A+C)x3 +(B+D)x2 +(4A+C)x + (4B+D)
Equating the coefficients of x, x2, x3 and constant value. We get:
(a) A + C = 0 ⇒ C = -A
(b) B + D = 0 ⇒ B = -D
( c) 4A + C =0 ⇒ 4A = -C ⇒ 4A = A ⇒ 3A = 0 ⇒ A = 0 ⇒ C = 0
( d) 4B + D = 1 ⇒ 4B – B = 1 ⇒ B = 1/3 ⇒ D = -1/3
Put these values in equation (1)
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Question 15.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let cos x = t ⇒ -sin x dx = dt ⇒ sin x dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFoAAAAtCAMAAAAZUYxJAAAAAXNSR0IArs4c6QAAAH5QTFRFAAAAAAAAAAA6AABmADo6ADqQAGa2OgAAOgA6OgBmOjoAOmY6Oma2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tmZmtv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///b8ZF4zQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABb0lEQVRYR+2W2VrDIBCFGariVlwqaktt6gKF939BgUYDKSYUM3fl61WH/BxmDgyEnEZ1BuwaYF799eCHck7cD2Poqw0G1jPl+RcS2gqcZDi5mqGhFTwh5YM0iGi6wlIt0dBWzA5svb0G+vj/rWTQ9nlJ3ifYi+GHqr0lL9MKKDi+2obnDuPuddFLSIVHE/SPVglnfbRmzv79vQzXQ7NItfrN8IcnxSOgu3hJkWO0u7cBZhtzt3LHP0Lre4Ab98c+XkINcxRcdHNbVVuWmE+zBbEvvoxtXPolwhj0UQ7d0xVu3VDGPxOSXWwcbbi/GityXYMuTEgTd9zshqtVj6Ot8IUeznXWNQnad5y37oQbHtzT0CXZPfgyhnix+dJOsAYa+blFu3cKvf1knp3GRxaRx187pbLxOgHBQ+eaTOmGR+ZZgfZ2ak0wkdAEsz9qKCO5l6ddQWWb7iRrNGhVtALnLel6oEISbTggkSep1QlCyDds4BmoRNHxFgAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 16.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKkAAAAZCAMAAAB9wf5oAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kGaQkLbbkLb/kNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/7aQ/9uQ/9u2//+2///brha2tQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACaElEQVRYR+1WYVPCMAxtAYEJKAiKKHOgMoQO3Bzr//9ppu06uq6DDu48ziNfdtva5OW9JC1CV7skBghuXxIcA5agg2tT9t2vijR23k7IjS6rxkmD0NkH2tQW8EYqeqCzzglIg/txxTgqG/GtRLobY9wPEdo4GOP6Gp61Rew04QtC9Ku3VncR1zuKlPRXBdr3jFAPVyu53dxl7sAD9drhbtRGyWiKIk501AzJQAD1HvhTWjSgh5Bun9l2FHcL2SjaJRCrgvm4IZFyckl9zZFyohFp8CIGoMOcz2Sypp77noHPwwZtQBEOlbtJRqARGIOtIAVmKgCFpVveGuBBIAWxo27aZijoCO2jNLL0THhk8U9kopAX91eQr/jB3OWsMtJ4zMEkjwskmnjZCkGNcAd5Jk+yIn8+qXcDtZZm7zNwAJKjyoHTSyFDKkjdG/VbSnoWnMaOK7gMHEFfhPEQAXwMZclKnX8NnDb1GXNyIvlQvRLUt6PwXIpUKxuuhSwkTX3gITXeI6n5EL60TOIepB2oson+YjwCp/mKNajPRM+yODCnbeo0GbFwDK7JCAien9ASKZB7N9C3mLhQkJYE4XkfVz9tRq1NJAS6BBXYXM1sH5ioyijlp42sU5Aa1Rec2lvGaTJ5MaZXWqelwllyasO7mkdWp7OFeVwfQFqusNXkj7CLaCCmuoWlvU99kCLKelfZWEAqi+SAepanKZtOr+aGMiAXGoDrGnC6HzMldUrn7N4gTjd9nlrQct4S/Yyy9lY4o6x3nrhQP/dt3fw5pcW7lB1Uw13KbuM5q/T7qY0v0/3UZt91zb9m4Bf8BUFVbc58xQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
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Let x4 = t ⇒ 4x3 dx = dt ⇒ x3 dx = dt/4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 17.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: f’ (ax + b)[f(ax + b)]n
Let f(ax +b) = t ⇒ a .f’ (ax + b)dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 18.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMAAAAA1CAMAAAAgXRSfAAAAAXNSR0IArs4c6QAAAKtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNu2kNv/tmYAtmY6tmZmtpBmtrZmttvbttv/tv//25A625Bm27Zm27aQ27a22////7Zm/9uQ/9u2//+2///bMinMAAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADMElEQVRoQ+1aa5fSMBBNug8ruysIyqrLQ1HKqmsB6SP//5c5M2lK+giGbV2Ip/nAWTjTdO7cedzkLGPd6iLgZAS290sn/c6cTsb84pfDAOL+U+g0AIh9B+DUCdgx0DHQMAJdCjUMYOPHQ8/lSSwWPuf88qFxGP6LDULuNJnAQVQPQMw4f+UERUUA8WtVXOnIDf9LDOzhiJlTAOIx96ArrKA7ZFLdLQCxP2Fbf6pXhFsAgusdI49rUyhAXmidY8dCl9PREBoOorCrgRzQaf+QTVICIE/gmGcH4Kza654BBUe6p9XA+afQ3lkXGeDYfPiEiTX00dgfskeaZa4Mski2lrXPvU878HvFPQCEGWQnJcIT1nEbpSjmLut6iEB8h7Q5vCKzYFr3SJ1YL/H9zva6Mew/WW/7F8OACiabKNgO8iXmX9nGPLmjgjEV3Vt7MuMb/VUNwKTvtaBVfGJ7cV55R9lYzFAMlJeYGRw9sPNRcA6XQLKYWO8W1d72GgGwEHRPCyvEsCVzaMWDHTTkKQwUPoWWPMC9A36JAGCOX++g28pYGozlKC2aUl7pDIDmv1pK3XaI3GNwraCJitn1TnyBgMSox2P/dsnCzFtS6CyASlCemIzp2aIpfi8AiP0Htrn4IeuqPuWO8R1tqQQoJJhLGQBCMWTpu6X8hRASVfhEvbESkbppBYDU/L2s7wVtHBhlE13x25/EqmQAPshNHO6yjcb+m4GKjcFYaTDNtCwhZe4ockn8N16hzNBNj18BFSUA2u76PVy9cX5XWryy01NIAoiU320A2OuIrQ9cGAGkHz7qPabOWDFQMq0CCNROzQAk9xh72UTpE7czAQCcubQ1GWcAdNNyDVCjSsdqNjaqgbA/RiZlCeCFQDLG87QU5lkR5xkkAqA+4rKKTcZZueumlSKG7BKP30bD3zg8s2767CogP6WOSOZwVdtHAqDX0weeUPO5CrrcAwayX0zGFN6iaQWAWMAYgJYxIN7zG7jnYaB+/tlWfFm8o34Smx9sPImBz1al9JGDqSkBdOJUw8kivhYmL65GQ++m3cPYS58H0pHz/y3QhhixyK3OpIvAP43AH7RQa/qcWPTUAAAAAElFTkSuQmCC)
As,{ sin (A+B) = sin A cos B + cos A sin B}
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Question 19.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
let![](data:image/png;base64,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)
As we know,![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ4AAAAuCAMAAADutAcVAAAAAXNSR0IArs4c6QAAAMBQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZmYAZmZmZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kGZmkLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u229v/2////7Zm/7aQ/9uQ/9u2/9vb//+2///bcXkEigAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAFCklEQVRoQ+1aDVfTMBRtpqhVBASZgh/AEGSdCgWU1c7m//8r30ua9iVt9rqWHHeOy/E4KE3uy+3NezdZo2jTNgxsGFh7BtLRdO1jrAOUMyEOA8abxz46QiP3mlRyGMG/AE1+vYZRi/FnRUd+0IAIhjxgMvmrmwG9l3WdKZKTw0yrQ/9KWjjkARNKns0H9F7SNX2Bf8x25yUdcnJm3x0MecB85CTIQoHF8RI1UbybRiUdUfbE0mEw5AFsRHkciI4ExaGmDHSkKAxn/sGQh9CRCUfCQwajiUGJIxNlUyC2PEIhD5pAGoiOtE5JZrFAkaFKDIU8jI4wHonOvKIjspKn7c4Wx6eD5sF3znaw7jMtCUNHTUEU1fOmVyMLOVNrK2zLY5ZxObHT/WMFlNbDQv4wlNPsaSHrMtSpyZkq4KSlJkEJsXyEPObypE2H/L570yGmdJ+TnZy0uhk5qadCkel1Bv/2zZFDhzzvTCVJaO0wxZioQ07eeiwZPGFKbP6aobkYu49Qw5PkQZGtRcQ9D23v6lZ89PlIJ2rwQpw8inH9GGtfcH/sEu5URU7cPk+R1ORT5JX8qUtH1s488uXWclaFNChjCxZHopFQXF4Z2fk8BakmBNmnJaKAsc4PKEqXjsSv1IYaSEprFWEeV+ow1OX7181e7sCMPDrQQZBX86cOHfKLP9016OBWpRVURbNNR34kxB6sukSIZ3NI4y2G26Xad+JDaCLI1VVEGsHw+LmL6XpxDhcOrNwgk+fW7/nu3IrMhNIWNZs8MlGtPMKcRQeWa3mBJKBTMPtStSXxtg50tCAj0mJ8BkHDJzoALFDywipSqqpa5hZ/oZHpoNqjrnUIz7Zs1Hh1oEPlOfUAMbq0DGV59luNDnO3GVNRjUJX3hYff2v784CXZ5j1aWT63vaouWVJ6CCSoOrQdluvwjzeM2dalI4m02aCtUHSDoksFoqsH5Ax9vpT/T8TOz88ElxcKmEX72+0GKrI1P2eqFegw7NY6MDEbz+mOkpkmw6d2e+2xZaab6P9elBV25RZR4+eqLnFktbrsAMdxYdPpgQPzh0UWXu8FnXA1fvYl6XU3NRJCvStI2uog/yN82EkKHIrXSz6KenccT41FsHeqzceXYdCayGrhGQqvXb4GI5KG14dos0vHTqJTMfSHnV1MOdZgBEJilg2rbxy6unoKlocAx0SD9wzLafhvoMgG45TATXsG5wmAsYCOVElxt2j1FMB0nWepZEtizribBg9gyldqbyMIQM+PTF0wLcho4OfsTidwM60AHuIfDCutINJp8hGALex2LrCjAERoNtYnMMP+96jbZDRHQYjaWQlHa1RsyY9IVuzFc5yuT1Lhy0cRebMol/b29yW3erKpQ77DMa/o3XiYXe0HTb49PSHfWoePqz9uI8zcp3d4NuHYY923uFZpHQNWcic2rzyWOqN3V6sOEIdhpkULi+NEVMJmCwKB3k9Dgc9ou6gO+aWshDPpvjNY/VUSM10kdfi6Jg/aejLjFmmlA5qVsIh941YWYtA38FVxoTSQb92Coc8gA42ufQfu3TxhA6rkAdE7h+z8y1y/4GaPctiQeiwwAIi958FW4j7D12eaeK0tRLsFxpCIvcNuvHKRd+BWvup91twlwB24/fUft0lLHKfacCrF1moV11UPOplKDyUkJPRCX0ZKjhyLzrGcBLcp+PgPrAP/EfIg0PfDLBhYMPAf83AXweJt1jZaIUXAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Now, first solve for I1:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
because,![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put it in equ. (2)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 20.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
let![](data:image/png;base64,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)
Let x= cos2θ ⇒ dx = -2sinθ cosθ dθ
![](data:image/png;base64,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)
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Question 21.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Now let tan x = f(x)
⇒ f’(x) = sec2x dx
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 22.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
Let![](data:image/png;base64,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)
Using partial differentiation:
let![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdIAAAAyCAMAAADfjaoyAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv/btv//25A627Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///b6lOIMgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAGkElEQVR4Xu1caXvbNgymvDTJti7t3HVn5l1a103tYnfW//9r4y2CJERAssNElj60fR7jegEQvMAKsX6rB1YPLM8D/75tmlfLg/XsEU2Py/HN7+LD5o9aHuj/evkPVXd3996TMvhCtpIqhljBkVvSm/4+My6Hz2uFtN+9fqDDPXzxsyVm8Q1sJVUssYIhl564YaLMiEv3dQkr+vvHbydkQ7+7NoHsdzTNTovDSOHrP8oZ5YW2bsQ1/a5R3+aVMogiVtDkSmlK/+bOyKUkrgUZJMr0uHwAU2m/c0MhF0f466e3zWfkujmI2ze20u8RblRLZ3IB4QNsbXMvPm2NAsvmh3iA8Li9kT5/18g/SWIFKjdyXNe8fujfKaBIpmAgfQLCuHBGXQcXR4yQHu7ed1NC2v5wq0dnv1OOzHzAhlCLgYvxwZAq2V2joweHKSAzso5bmSsksaLF5ELHHW4VXf+LtJeSgCFIm4BRXEohbZvm+qFrFOC9jOg+SNvQsoAsl+HKZxNCevzmb1N5D7daL0OLSXiML83GvQkpHCfZkMoA0MWKnFyovfNLTpspCcrYWu9Kk4BxXEohFa3UqGUet2ouQUI6kDmBqB1FjQNBd2MzYW9he2PKWvQYwfjSkLY24zRbVrp2+H+/vpAFmi5W5ORGmeJz3WZK4kvUlToBk7gUHaxWKPnZN7IsIjtBSJUIA9P5MDEG19Kq4Y3xJSF13hSaDQmpSulrtT0ii3XjWRaYQC7Qriu5+ahih4IHErAYSk9wuP0qPWCQxcF+rmyEZOmvkwrv4aWbtoZSExgzrkX7MMeXYxvqrXd9QqZHaa/qBFlsUMed3ERsJqQyEbzLCSDpofSUQ7GHzPHCDR5DnGCUyilcfqouufyV3qRqAaM05ouMC5Y7Y6PUL48wc2LMiFys8A6jD6IslCJ+SI/ffZ9f2UBNMdn8kB7f6Mlfr8xcIOlawFwqIr7IuPbGV9vCXCrHnXQGZk6MGZELyfS4B4W3YG2w0gQJSA6tXF3rHVn6wWSLyeaHdK8nGa3cTXWJMaiW4zZY8aotAgARrTn1tKt3S4YNXx6ZTQxmTly3ELmQbN8olWoT4+fSUWvDOWzSXNq3UqHRGn+hZSlZ4mzu8bCtWkd1CGD/zdAC9qUJHzBOk2qS0X2pOWpolSswcyBmVC4k63ebe3mEId1jM2XcWmmkL8swAYmjVB6DbWSCN7mYBpZlyOAY/u1WzopXPxG1mvGidsT6L1XqVO3naAlPj1I+YJxdgeiQ4qdH9kDw6l6RIeZEFdUsIFO58Uz+p3TO1Y9uKViwtg9cOeNolxGJM5GSDlUD3Zwz3gxbCcVUcwpysWNPjA0mYMnop/Y77UDbWf1Mb2KYmfKsB6laP9CvncAFJYOPc6/JEMu4L2UlLv3K7qmNz4uyh5EpnAS8KB8uEezhy6GpY4n4LhHTcLp1iegXhNlcyZiPewhwFjfkzqfPougihHYbews6RPkx/4X4+DFNWIIu4EYf0otI4MWCXAvvYkMb3kUuGORFQVs3MYsP95Tzi/BVBp2/9vEH3VJ5Q+OeZARQGfxVodJOGWG/d/gqo8w/NKHXPaQsW6qHLwqVwP8koE7t93Y9zXn+6HrSN7fXvEogIRXDK4HBVne7XmoLUH3HTwDqxH5vWZkMwDw/DGnQhF7xwo+CVGRa2x1UAlLQb18L6sR+byHsqwzDX2wXt01io8+KzrxooSINGjztqz0DlYzU9dvXqkjT+r1l4tpOX/eywHXo27gkndCuCZ1553vCMFORDiG1tlqoZKS1oU7s9/avMix/3BQ/0tyOPF86YfDyoqhIww5L/STDPgyiIg367etA9bcyrH7v4VWG4y+wZ5rbzx7DSAEVadQ066ESkWb67R8Z6dx+b88/2i6ONbc/JlgqUqwPmoY0fLY4rY16tk+obeTBQ5vwWZBvLqY3twP22fbTBVCRYiF1/ONI5Zp36OOvA3Vuv7ebYajN7WaZX+OjIo3nUmcrCalpCzZ9/LWgzu33Nvz05vZJ7eInyQAqUqy1nYLUnL/YPv5aUM0sN73f2zzYSzr00eb2Wps1t68smCrw1nYKUrVB9/321aDO7fdm8tc6UkHPuUYqQGQrE2n0NOMklYYmhLn3T1KPx18tc3Upov23O85vsa1M/opQCfcLQ3JkrlI4/M/iJsaiTW3lIGX8Z1a0oceimnsLSOeveomoxunEJxnOnQz+2lBZGbASrx5YPbB6YPUAzQP/A4xNK+I0DVWAAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfQAAAAyCAMAAACdztmlAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv/btv//25A627Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///bKfLj3AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAG50lEQVR4Xu1caXfbNhAkFcdWj9RJnaanqzQpm6ahXUuq+P9/WnEDC2CJXVkU8WzyQ+L3DCxmdnCT46ZZniUDSwaWDOQy8O+7tn1dS2qqAnP6pNRC7/D2Y3O3+vP0BI+JOCOY4e9XX4iQ++vPxJJRsRnppYB3X80meprrE4JhqDNs3jyQldx98zuxbC30MnD774kc0mL3Px7RX4bNpclwJtc4mOHu67Z9WW5vuBcrlio3ps6waeWzei2hDJtyCnzYZrxjyuZX1zps0pVG6DnYRTVM1umdL414B5b0YTPWjeFv9+/aF9RJMWh325r1JJNrAAa21q0+NvtNdikCBbv2ttnfKGBQHRjucHMlZPnUin+bbZ4GFrbpba9VrGDcvn3zMHySMJn0POxYIyzrx8+KPdzGMUTfXX/ujxG9+2WtB1aaawgmEl3K07e5PgnVCcoBdWC4YSPLHW6EfvrH9EHDjnSm3VrGGt4L0aehF2Yddr7CDNG17eVD38oEboXm2yCRIdGgmAkYd4ljRD/88I+e302ucTCZDtiJXlaGJSjpzgHUyYsuNNqtVeEkbtq+CQvHMCjWu6noGHoyfpmeyzpvqHcCmsJ6uJErGyJ644rZTnQK0furRqM2ufatxGCSpO8/qJ1zEZYooqcgoE5G9P/+eCnKbY1QcdxUdBO26cKpISw2bNzcx6dnYBfpOdEpexE//uVeKr+nAESTYicQXYbQ+bC5RsFErck+YTZIEfpEHZtwoE4suuzul7ITYUBGwoaLelhMLRf64dJzw4CRddD5CtO7HGXfiXk9esTEYh47R4XF0t+KJZa/pu9e2UXUZiULJtda09yvzRzh0ecK+hHQGQ3SUmr2HeSo8iwCurSwci4GKcuITqdnYdOzbukV9dYF/NoDK0S9Oyp2gpEuthLikdr5HoOAyazp21btAcdhBRuzMCvoRs71vihu1D4SFuzeg+mdTc/HJ2edJ/rhp58Jx5QmLvZ40Q9v5QlabYhcrjEwGdF3auNfgNVd2Sm2KYmuRMKARO2HYbE1Xe034PSeoLWjLKbn4tOzzhJdHCnUOTV94JoeF3u86Fs136rG3aKHgYn2F1Ju1VsS9BCWOshs9akwXPTQkW53AHFcNOzhJrzMAcX0VCSPbDx6YvaysAv0wimSs6YPnUBmZspId7AVTYolonOv7c0UdpCXJybXOJhIdNHWXh720gqgoDrHqDKycwXqQPD6cqaTGhlQSVw07Mg5fdisbsWdj8DKo6dPlxJCgV64uMHON76wiyvIlRjprV4f0TU9UwzK8GEtVueL38YbA7+VjQrZ5H8vvuhcj4CBKu1lc+LWtATL7K0UN/ycbq5hL25lMXWNksYF7Ydhx27khr8EzItf7W6VTM/GL9EbgqzzzukMnSYsitx+nrBF4pUV77xbuHt38Kuhd8KEPj4UM9f8BskjYZK3bPXQ42duwhqsXPNxMF5DTfI+vR56/NxNWIORaz4Kxvt0fnBSjSdOj5SDpdCkGdh9e+QnPZOiWoJPmwF/szhtO0v02TOg303qh3ttMgn4/GuTSZpagooM9Cvzltz3g3P+hGhwTgjPoy2QaCf6MgSedgaW6f1p61tgt2zknp/8y5Ht+WmeMGZcDbl7rNB5Ra8//zVYRJ4OXWx+rWMp4M6oXxd32iUwNE6EzqtyfZqtZIbhV4auQKHcCfXr5I687oleVzu7in83ZX7K14/eNiO2khl0DpskUW+8VSfmTqmPWmpm5U5x7WSNE+Yr6Xx9KDpmK5mVOM2w1Ixwp6ROfbNkrDfEF/jTZyW1Wug20Q/ebHc3xjJdn+7/IL/Frod68BW0sfBq7tTU5S010/PDW0isFqYoKrqZ06yxzLp+rCsGqZ63lcxJPGOiwbDHphHDnZq6+rhTDRz+Q201YTmXm6kfGy9G/B95P+AM+lOpB9/gA+7k+llLzQyEXZM5J8m4XUV+Tu2NZbY+3/8xJ2vVNpV6KHrInVo/tdTMTR2zWuAfscNv6F19aLwg+j9mZU+lHonuMBPrY96XGbkTDRwYcTdcIuPFiP8DePZnZE71rgD/QAiemDrEUlMD83EDB26csGt6ZESh2UrmJI6baJL9SLSfsagxl0r93DGrBWpXiYwTuj7d/8HxXUzcJ6jUvXMRgifVRy01E5MbDY85SVC7SnTQ1qbexBWD+j+qO6cXsDe4aYSUOtRSM6fo2N/RQTHF10pMq0Y1t1Jy+8410EfgufXr4c60WiQjlVe/ooFO+2NhYeePwfOoUw1PZ5kCCK+KPI6ML4RTn2ErOQd3DvTcX55j1a+L+2NfCtPr1/VOWW5A6X8A1L9PD7ojo3513M8xqpY2lgwsGVgysGRgkgz8DxOgO8bNE+8NAAAAAElFTkSuQmCC)
⇒ x2 + x + 1 = Ax2 + 3Ax + 2A + Bx +2B + Cx2 + 2Cx + C
⇒ x2 + x + 1 = (2A+2B+C) + (3A+B+2C)x + (A+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) A + C = 1
(b) 3A + B + 2C = 1
( c) 2A+2B+C =1
After solving we get:
A=-2, B=1 and C=3
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Question 23.Integrate the function: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let x= cosθ ⇒ dx = -sin θ d θ
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 24.Integrate: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUcAAAA4CAMAAABZlMr5AAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kGY6kGZmkLbbkNv/tmYAtmY6tpA6ttv/tv//25A625Bm27Zm27aQ29u22////7Zm/7aQ/9uQ/9u2//+2///b6cz/1AAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAFPElEQVR4Xu1ae1/TPBRuB8JEBR14g4msiGXI7Jbv/+HMrc2l7fI0PRSV9I/35eeSnPM8OTm3JMvSlxhIDOxl4P4kn31NHI1lgH27ydaz1dhl0nzOQPU68UhgCNvrS4JVXvwSRX6YeCSxgof5Fck6L3mR3fkqqxKP403gfp7ynvEsphUSA4mBxMD/xMDDx8jyo2tirr6n4AfWkz1c5PmrSFCxmm8v8oOfMZOjJ8YIy7IB4or8Mtsu4lDFKcdr4dO70pXIvt8hi7kTq7P2nN2CG+aH0Fpk4oyg4pj/XeZXWcEVOHoMaUD1u8fjbRB6Ldie2Mz6xc+UInW3QDCMFNdLwobziOpAw6TLYyk2E/vsiWypasHdedM3g3gcKa5f0UKeMkgHDG1wlMPjkJ6XM3FjvINeA8FAIa4ToK5NER2CBIEDHDqkbwE/ZyJbNv6gVH8hGCjEdWlba4PoAKINDrPpGGIfmesQGoNc65gDYKAQ102jNgdAhyA/6ACbjhIJDfXCLo+7hTLDsg7dAAYCcZ0oi2MdpQEdUJqC4yw6ai6CcxRjbsJUyD3YcBo3MuaEMRCI69RUbs9GbGtYBwwqMqo011KbQTdU1kQhR06WSaNMOQAM48V14pPeghWT8siu5xz3ob4p9Sxs3y64E8XIau5mnmFbIBVnlBXpty4BwjogljZ0DFsOcY/+6mzpxvogBlpxnWCDOgylCBq/WwzIetorKgfZfApDmff6Clpx1DyyZZ5H0mGfTLi7Yp0nN+5oW+h3grTiIngUfaHZaV8BHr/NqiYVX6u7Utd9++zaiztBHmnFATx6IMr8/SP70XtcfD8FHWk5qAHW0QXS9fOT8EgibjCP1VwcW/bNalRWb6xeVzyPtkH53TSAR2NfEpNjjxU/Qm+FkuxWJAiynUUrbjCP3vFRlmRZ59/IYzXnrdWl8J/FwSq7V/7jeXlkUh2947qNz/9niDQ86kTK+RU9mLT2KPsRogcjldMe/Hl57EmJylkdI/bao0et2Yc9BtLaDjPLuY7pP9eqABT/1TzKjL2Hx6Hi/PE2JkNWa9VxPO4NOrQGYvlHxaPksOAHZ53O9b59QOyRk8l9kHqQRrttg+OM2FH/o4kzNhER/rE/f1QVoOxR6yavDI5NutrqHUWkq4N53MhLuP68hyIPd41FnsnwW7weHgVbQuetINNqm7s8usYRIW4wj2zJz0V/Hk5RF7abOX3AzPWgSGmci3DlHzcqlVjzrPFMVGClDAPyz6YuJBE3mEeVyh5+IbmYZesT8/ZguCVb14Ocx64+hQdvdyHs+rd8IUkrzgiyME3W7ylmN/zA6UMV18iqL1mgvplyu3X8jmnT9YkzPFqYpuOxfnugImjMY446ckB9XOnc2a2SQyrO4tFgmoxHKb1xbGCjn+e0R4/c0cnQU18POrWp+KEbg/Aj+alqB5CK8xzI9O8AttcaVn3eOj22848i9dKRp7ke9N0jcD+D3nNB4hwFa0zT2aO4mDKtTPAiVDhSdZzt60HvYRCAgVKcxaPBBOgQthp0xMO8cYvoxXw1fyevqa3rQethihIMYKAU56LVmAAdUJaAcSqzV64SvJJoNe/sBBvmkVKch1NhmpZHK9KCFrL79NkL7S1zhDAQivN4VJim4lFZkVPoIgbJi1Ivie6odyAM0Ls9SFzDo40J0gE4saEhvMZcqcK3+YCHnfKtguUM+NyOWRgGMnEWjwYTpkOIJeD3rXhPIavd+gs/NOYV/Izbo/1o+SnfNYPiDIIG07TvmgG205DEQGIgMfBvMfAHCyy3L5aQNH0AAAAASUVORK5CYII=)
Question 25.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 26.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHoAAAAnCAMAAAD3l6z/AAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZmaQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkLb/kNvbkNv/tmYAtmY6tmZmtmaQtpBmttv/tv//25A625Bm27Zm27a229uQ29u229v/2//b2////7Zm/7aQ/9uQ/9u2//+2///b/96smwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACoElEQVRYR+1XaXPaMBSU1MZW2qZASq+A26bFvTC9YkdY//+HdZ8kC9vIxplC/CF9Mx4BetbqHVotjD10U3NOFo+Qh58371bl5WoEZMb0g4RGtsvLT3/GyLg6X+nkLFDsLMrH2A9hjgg9SsgbyflVwaMczzcpltjEDylWSlIJ9AfOozXbgg+e46vxrU0P2zDeWjJDKLDaK+p8ybKpSXgmrllqal5EeTYh5CTO1ZM1DdtZzJyvnx6GXMQ3CQW0ZzoRbwFioN1DpX98RZ7oSj9kj7AF4+unB0HrMK559/ccWW5Bb56a6BvQ9IvxReLt9CBzawR8kVuduIT7qG8/4gh+Z6ycxbn+mtOwTWJKNPmyajq0HEddG1aILuK+ReecrZUU10ryGA+W3shYp2g8hD3nxAJ07aD21rc2HcRuQaNQlVuKtU9oSragUw+9eTYWdDHFSTqVUV0uEHUKMsgze4Z14qIu3+TZ9ItP/nH3oOSC6ffUZilayx0qD42tcL6r+3GhDR0VBK0TRG2z66HRrMRqzPNaxW//MFb7L2cEZttMyYuJ/b0GfdxA66vVoUHK7jTfO3T56rUrK+X+dOG6lXHJ4JOtNSQgrhub8PvQv3TzbV8CWhNtFcSLBI0Bd68w91GfDea6gKP+zMXkl+SLhAtEbc91OUMWMty99hLstj6ua2iowaRIkARvou+xXq6rQw8kxfLFOkOpzb+OtLfme1zXdc0PJUWQCOmqFnRIdTmuq0kzqzD25FtFijvP3mQ2E96huizXVdLM8XBIvjlS9J4HmjeqtVmX6rJLGGlGPUq2DMu3muehY8PKOReLyqtLddn5SntVtQ7Jt6bnQfSdQ4fqsg5ee1nooHxred4BOqy6XCRemlnokHxre94F+r/vqTLwF8C5aUtomyhaAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now let tan2x = t ⇒ 2 tan x sec2x dx = dt
And when x=0 then t=0 and when x=π /4 then t=1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 27.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
First solve for I1:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAAA5CAMAAABQ3QrxAAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLyQkLbbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2/9vb//+2///bmfqAmAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEc0lEQVRoQ+1aC1ebMBQmOF3Z5qti3bOtOotO0W4rMPL/f9juzYtAQqQF+tia4+nBmpt8uffmPj70vP34JzSQjwgbkx09zcNjNPHiwY6iR9h7/Bs1Hp2i//xZbBREi83zcOIlwfnO4m9xdBD9BeFr2G6JTUrnl3feiz/bJITWe6fv+sNP52DfwxXXbygcX7RWQe0CERl7WXjwZJlA7wmBnXn2hWFOcQhrk1/6dP8IE2tsLQ6iCw9+XMMhXIjFfcLn2yQ2/Ol7m1HM4zDh7JoQfwghNh0R/xtOggfiw18SgJ9MvIiQo0XcUxUV2fwnOpIR3x0CUZhOjxb0BgTSYOzNA4CNDxkkjjwUtV8EQQgzYQ8jxQ2rg06l77hDIBPOQ5icniw8PDSdgk8WpxcL4xH7ucgFUv0MaaD7fm0IFML35PgHSLNzIHb+UBppcNrLTWDqqnFr9XWd5pTwywdy+CS8hRw8WfB7cT9pLBpYK5tSTKoNgZrwPBgI/StDlLSSf/xkDdMtL0SM1zQx46SurdoQKIXR9dFtlDlMo9LrWR523wUxx6aWOI/xQgwRAk1FKWEWbUaALoF0SJ8hgMb48FDkdbZFgvmw2wFxGYexLp0qY6sQaOyshLPrgBBWYT8HxP8qHg7vlASdEh/0b9mo2+NoG/bhrD2BtSyb22uiXgEkpfQMJiOr35c8VOm3V8ylxct1TKvrvhH85UKgJjE1U2cabED/u4wf69VTqKVkoQpR3V4YNNN/0uLuNNuhWh1BvrjBUlwVqhb8ImBDwH+tFlk3flavsvurCtUm+lfNYbU7tOIvZnf2JKzA6z3u/7JQbYK/1tRr1r+OXxaqAj+9L7JAc/+Juy9VXNdCxy8LVY7/+QzrqqXHmvFzrNz/ZaEq81dj7l5PeGvGDz5z52VXgF8Vqqp+WBF/L612LR0KZJM//BmQsSxUC49x4qfQ+Nn4t6jufdH8yk3WubvEVehQJ/4I7TY1s4HWvuh3JxtBc6t/UaVE0oCt5aI8l6RDafTWQd3XUWh2/On5Y+zEn4dfGP7EkR+XY1GA83q16zH5K639qoQuN/7ogiEH5pSAoZhzIv8GhT00Zpw+4VxAh3xcdnv+WI2vmMTtMdeJPzlZcM2zTwiKC8oMmQbHM8GySi6gKz4Om1Lz3VB97+DCn1/OhOcU/sNqAvGBLTynQ7UyZ+nUZAjMA6PXtfFPXE7DX83mjIsD5DG8L1P+X+DHNTUuoEM+zuQ1rJRoFT/+rscfcHP5qp7jp/Mr4CWk/qs66Y6PK3OdCCtBi9BbwYXrFnPfXxl5lP9L15Ekb7FUJ3wcp19N/p8Ra/FgYcbqJfCzQ5T9p4DfDR9HMXVlRrBhXoHvfU1uumJ1g9Lnf0eLPnyHj+wz3l+moJKVu+LjslvwUHxxohn2cpag+jGaeCy/qUFxNnnDXrDwUcUPd4AdAMqZCaaB4e+QTFK8BSX2rU8+DjZiwd+CXz/L1j/b/WfrYRcAoadestbarsPBf1754+2CtEez18D/oYG/f2WI2ttgs2gAAAAASUVORK5CYII=)
Let 2 tan x = t ⇒ 2 sec2x dx dt
When x = 0 then t = 0 and when x = π /2 then t = ∞
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put this value in equ.(2)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 28.Evaluate the definite integral: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARgAAAA/CAMAAAAMjieEAAAAAXNSR0IArs4c6QAAAK5QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u229vb2////7Zm/9uQ/9u2/9vb//+2///biJYKwgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAFFElEQVR4Xu1bD1ebMBBPOv+w6bSd3ew2bacW3RR1W4GR7//FdrkATUiANEGfLdzzga/krrkfl8vd5UrIQAMC3SKQnVOky27Fbr+0u/vwkkSH269I9xoMwNRgOgBjBobN+VL6t+reFLdcYja9JHEwHoDZ8vc4TH9AoA8IxLsQJ7JbSs8IEXEvUBcvrh0Yvge+cQrPCPy9Nr19YJIPD92Bki4oHU1WMU+5+OUxoBOUHlJ6sIqkTKwCTAKZ2ghsiN9P7oEhl2Tg7G62zZLCgyJyeTyio+9eX8vmByt2BQKTgCsZfFySKPc24WhJZDBUYJLggqQQR+F9/u4BhuaSAJkKp9cM7ZnZvFhGbHFDnmASHpRNQVhyUgKD6Aj5XNNIWrEqMMXbCXkSy1EtJemcHvPbhLWYuOBJ3nsBQ27px18oR1gMXFBD8dGpWFW4OnLK30MxSNzxWkhSOTfRzHOssn+k1xee4p6O6D74LAMwJFKsUbEYFRg253aTS+LzUTk9Z2jLXvgA8Sb3fIEh5DkAtQzAZF+/ge8oqQGYAiaUxC1I5bTVzHOc+jaeufW7E3cvhPsLHRi2WGZTqQymACNsRLgTgWopCT6scLpPbyNO7vMFZZ+XQiF3wk3lHJTEBYqX3IcxHirFPJDMSXW+Eb0g7G6JI1KOTimJaJzu09uEk/G9MScIOjy363QRUAqFiwRul3jJphhWszkdgcXg/4IqcQx89/4NfPwETBOwmkKSgXMT9dzHysC4S9lBzmwqe8QdVFBVCUNyK8qmZeBrNX7bB7Vnt4XH7Rkw1rtLEvTLYgZgDGueZ+6nEI9omb7JP8S0N2ePPDRiV9z5qvm6lrkhTj0CBjN4dL7VTN/eYsrsdxf+KbcZHlwKHyNl+nXbbH8sRqSmufOVM0TzUoqk9GXbY5Tm+cvAWOTr/QFGZPDCx1jk6/0BBspdNySdATBW+bpcpzKaIlT2t5wKteD8bDT5HdALLdM3KR62JFVgdbvteuq0W9epzCOwktZHagMmNgTG7OdJh2d0L4d6NOYnd27E61SN7ZrQflYlNv9ksKLnWfOaa3rOniGL2a/wWxcI6jVPji2LL7oIHhw3tWtmXzTbWJ/QSeLSc6oWvCqVS+25MpUQKr5ptWLWATAex2SicF/flWhwMbGh5JeM76MmYPTnKjB8Eq37o8uaiFyLKiIcrAdGPlQVEytOOqrTbASG691WQi0sxLIvwK4LwPlkFVOHhnbNW81x1FV6vIEJBXKWfQGWXQDGdW9jergu6ts1DS4mrjn29wWmANyyL8C2CwC7BByoZQ2KzVpJPwtgqjmpBIwxXW15vn61Vn0B1l0A6yaXjdBpa2uK9O2uzlf4WYzsuWz6Aqy7AFyAgSPZuNlpm/KBl1lK4aEcGrX3BRgsBizC0AXgBMwUur9AnKkrMZ1hocuQD7wIMLiiYzy+tesLsO4CcPUxNQsvGp/jVA2eq3ZXUp2ytkibelxwU8ViAC+xWfUFWHYBlG1LG3mYpsEYVRjyAXMcw67hLJ7uSQ18KjD680rki1aLwNj2Bdh1ATjHMcX8nmaVH1dgOPHDlCuaIt/O3kfXgpwj3zyavdXTQjB9c8nBOWbqWmkLeb4GY/rBH2RRej6AczFn1xbTfPUhHtl1rul4dqz9TikaHdcUEvpQj0FgkmDy90/eBbd+qz3rnDGZM2++I7qbGn5Ry+aTVV014dX9wpv6QqivYUfgQAMCAwIDAo4I/AdUCblSVZRxCAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now let sin x – cos x = t ⇒( cos x + sin x )dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
i.e. f(x) = f(-x)
so, f(x) is an even function.
It is also known that if f(x) is an even function then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 29.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAsCAMAAAAqwWZeAAAAAXNSR0IArs4c6QAAAIRQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///b22MsVgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADSElEQVRoQ+2Za1fUMBCGkxWloosWFOtChbKrveT//z9za5tbk0yn68Fztl/gQN7pPJnJZJIScnn+3xlgp3tK3z9tDoC1i9LX9IH05buXramwdlH6+prjNPSHCTWUlNKvEczXG7r7TkjNh334Ex4XsguZOKyekNaFWnJVucV+PpLjTqTsUEZHOnYhUHIsSl/b6ZdwVb6v+5gB5dgFQ2H0XWFlX2r+hW/94UH8iOO7dqFQGD2rnPWTjlRNr9JQnl0gFEbPKlEr7EIRX1Ni7ElGN4bv24VBofT1tVvAUpEa7p6ISo3YSN8uDAqjb0RUWisBU1DktZAlPQoVsAuCwuhlFWM1DGrybhk/ZBcChdKLDdTdapORyoAK2YVAYfXeu2Yo9uvzy/zvZv+8oqRAUM44doJi1ReriHSf7A0tZ0cz/BTtl1FXG54hjr04FEo/QumNwmiYVR+hMpYmN1/XxaHUS/f0TR0LgLsrSj9Ctap7MhtmWZPmJ3/1qVopofp7qtsyC4pVqbDF9YnU1a6Ou5/ZMKtQZRSK0CuUU93+ucFALenzoKx51A2zysjf/GB5q+Y+3XuYU6DTDwXF7QX1eVCtPF3oZ2yYRdiGu8yjh/OeaU1sC6WrP1/lpsMuo55/E2qKWq1Dk3X0+DdQXoh0IVO1bHw01Dif/M9zwzxCNTKTpvRzZ2vB7lL6eZMN1CdSz3B1jpTRMGuoo1xSb2NNrUw/o2GWpZA0iultQGWEaXZ1WkdGw6zWesuZ2tTRw3/XmQpFHGoo1XHR2afMhln+Lm+bZIeTV9Jnu+Oa0mUqc/PN0y+wOVBk6ijmRn5VR2E7xQ4Ft3clzmOroJb0BhQ73ng3tE7vZ4x2GopIpMJ2daRGi5HeD6Wvd4+kr+xda4suPWw3HwqlD9/Qjs3P+vNU2C4AKnhznK/nfTj8MjOrpHt2gecphL4/OCfavJqW3Kc8u3kbyjQKoRf1eW9fkm0CFbALgsLqT8V50s+1C4Lig3H61v5ws0mkBIFjFwqF03eFVVY2g3LsgqFW6tWZAvh9anZuET9oFwCF0jOx7/bV2uuUCFTALggKo+9FJ3brVr/E51HtXezzaMguAIp/APP9gugvYy8zcJmBlTPwFyWdb3JxVEoFAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 30.Evaluate the definite integral: ![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
Also, let sinx – cosx = t
Differentiating both sides, we get,
(cosx + sinx) dx = dt
When x = 0, t = -1
And when
, t = 0
Now,
(sinx – cosx)2 = t2
1 – 2 sinx.cosx = t2
Sin2x = 1 – t2
Putting all the values, we get the integral,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 31.Evaluate the definite integral:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL0AAABUCAYAAADXnDZ6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAlxSURBVHja7V27bxNJHJ7NtTzaAzK+iuNK2HE6RMVtluMhXWHBZuXmAhayIusuCdoCESddJO6ogSt4NDz6awhU1/DoT+KRP4DHn0Dw7W92Jl7bu/Z61/Fj/SF9SmJsz8xvvp35PWfYxsYGA4BpAoQAgPQAANIDAEgPACA9AEw26Z8yNsMY+64VT2cgLCCXpPf/GQuC/+X/3PF/3THUTyYW7kFYQC5Jv75iH5+zlxbrNfuEsGqXlyy+wq2lFQgKyL1OT6S3nfopIr1w189BUEDuSb/uinNEdpAemBrSL1niil2rn9CkJ10fwgJyS3rPq+yf5/wJkb5m82Xhulds212EsIDckn69LM4yPv+ssrm5jwzbAiv8J8rrZyEsINfqDQCA9AAA0gMASA8Ak0n6zpybVkBgQB5J/7UbIDAA6g0AgPQAMKGkp7QD5NIDU0N6InzdEeeVHr/DzEsPGWsYEBaQW9JTWjEXCzfpd0pD4Ix95tbSKoQF5Jb0tXL5JOXd6L8p05LN2s/DrwFArg1Zyq1n3N4C6YGpIb0sGbSryxAWMBWk97zy4WLBvo1VHpgK0jcYM1wh1sr1+iEICsg96cltKUsFVfGI8tsbEBiQS9LTCn/DOXGBW1ev6QAV/Y3qKSC3pK/afLkz2cx8BzUHmApDFgCmkvSteThIRwByTnpp0DpigTP2xf+9QekIMGiHPEHNRQdyHwbpVeKZOsiVbFz+mc7DgeCGR/jr1dOCM/4Wch8S6RdMfkuedGbPLRYY+1goWghUDRHyDCLpSOBfQPohkL5eLx8yGX8NYY8WmIdhkp5SjLGtgvTTRHqZXenr8VlPLQ7dbAJDbAikb0jDN7mXbVTz00gR5VdG/UxWL+Kekz642WSwOilrvSJoZlIfqOirjlrLNPshPX1fzRKX5+za4ijnJwlqvp045yw5SctR6SGpXrTOmZy9yXpRSE/SZ23AF+pNxgof7ZX144PwZnjV0jEaeOBN8sHNN9bF6sCPE2d9rpjpZMPuxR65oq48Skp6r1I6cIbzx1T11o+zYZDz0w82Nyv75jl7ZszOPy9VvAO93q8yBXYGwcnY/5AVU8o3Py4rY+C+Mz6HyeEz8xv184Rz48KA2zLpCqJJUG9oFbxk8luTWPdAD/6McB4kWWAGtRD3JL2/4jwYB+HQymBzY4vbzppeyeo156hcLSTxxfag8oMCErGHo75vS+5sXumIT/o3p6vXRdxu5s/V6qRWtwXzyraSLK5jQ/qQXjoTpRJEGUrhKGPTOOl+3Ii+BC5SaLPseVgvLXXox0Gf2l434sZz1eLXAuHqTNNmvzr18NbxphlbtzFTfETvalGZrlToYzJjOy4Ldljzk0XmAZnN7bLnHe5iv81EkT5Nu71J36UonPTIeVG4KyeFi5dO1TklhFsP698/i8LfYdcnfcaxxArn7K1w6udrrv2Lr7O8pKgvNy/dqnje/hRbpL89ig+00pM64C+J77Xa43fjG237+nX/b4osf4rSYYNVhz9iuxFoYyesX1PfaTxN1Yp/np2/uKGFuhdj6wW5ysfscsOanywyD3Zsco93nrpB/RPceKX777riSpj0advtIczupF8IqQBEGGmYqZ2BVqlmh5qrML1HpzUUivYd2/3jTGDNS0Olb2/R7kofuutW90W2PWu90BMVpFWI906tfrTfbbS5o4ht/XnX5mvhPg96bInHHjNHw5yfLDKPGkddqnXGNrddqc6SKus/fK+i5qXfdnusnvGkV0/TNhmQeqWTrwlnrZvqEd5FwgJUT/uXfg1nMjg5E6/aVzpq+0yg70sjt6K8G0m8FHGkJ/tBX03EVLFN+/sGObYkRi7NQZQKOor5ySJztVvLHUte4u0/sO12Ssi5spKl3dSk1wYICUy5DCN1tuB7kgu1H8O5oW44j9Nnm9ucuV0s8sdJq7+6GUw0Rl+oB5ecOcfv76d+SD9op0C37x3V/KSVebgfoQdsJem89NNuatLLLc+du7jrNuTc1wGXFtqNnb0iva7j7eWmU4JSW9/m/iykJ6NPpVp/In84BYLGlfSjnJ80Mg/3I07+vbw3SdvNRHrtNrSKhdvKuPsWnH3ZXFH2Qqj6vM0ob07U+zjn/9LEJ60HiBJusOXyWzK9Wm2bUe8bJ9KPYn7SyjyG9Kv97MBJ243thCvY/V6kD3+pMjRetgtrL4QqA0ch3TTs3urQ9/mZR7X12vek81E/yN+dhvTN/rn3u71vqKTvotOPan7Syjys01NKNennzFx4GDMvq1naTe2yJJ3REtZaOIQcGJXGl7A+JQ2STqGuphGqNh7Jddaeq7JS+fUnIezdEDwFdYq8+EgbuPowWtL5Sp53JCHpV3W7UQJXRTYtFWVpx5YlsOPP0Yv2ORrF/KSV+a5BrQxX9TB/aP+clnewWzXVtH7bzUR6GUkT7p+lSuUAEa8a+Izfaws8iCb6K5GyqilwQHrxJSloHfxpGI2QJ4T0sahcjPbSxShwu7asfc3WLHuhv18bvTroJNuoesdigyVaaL5wyRPg2vZvtZp9MjBcA0Fer5Z+LBYK/+gVqVotmfSdacaWBeRKNIJVzRzl/GSRuQ6w6fkjVOW42E7QXuUgydsuFu6oud7RXrQ07aaOyEqh2q4kg9o2gwCI8ou2RxMJlEIg3X4tr1WXO44dUQOKMsri0UyaCidyaUO382iT7klWQSJW65h0BRl9luyJIC+GvZN/l8uLacc2ABXnQ/uWP+z5ySJz5VP/0O52bsqbfaWqvYADJHv3d91+mnYnJvcGiIdcFRNmK44bNr3K/vlZ4/kwk+VA+pygma04OdclSRewTJYb7O6XmvTacAPpJ2TF3I0Y+8bgHuT4DBqev8JTYJFz+9Gws0MTkL7pogPGH6T39opfjANIXx9VP3sGPkadUw4AID0A7BnplSts0OmwADBWpH8aqpBRBRVPcN4KkGvSBwlVrEFh/rJXPjJfEHdxLj2QW9I38x10WN/Ywa2CQO5X+vYwOwQETJUhCwAgPQCA9ACQM9I/zXBIEQBMHOkpMZ+O0JNFxdzemsSUVQBITHpZAC3YA13FIg/5QaYlkGfSBzk35msdlAqqg8ytqHMGASAXpJcpxaG6WF20ixwcILeklxVTIXUGpAdAegCYGvUm4ZmEADB5pJdnvviGrDJc404FBoDckJ5AlfXcqq4GBwT9sIpsSyD3pN+trA/dwgEAuSY9AID0AADSA8Dk4n+LPidWuEVj6AAAAABJRU5ErkJggg==)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQMAAAA5CAMAAAAFmb6GAAAAAXNSR0IArs4c6QAAALFQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLyQkLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2/9vb//+2///bNH0rAgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEQElEQVRoQ+1bi1bbMAy1A4zsBaMjwB40sNHABgG2Neni//+wSfIjdmoXA2ddl8SHk0IjK1fXkiyrhbFxjAzEMNAccxrTGOGeylxdF1NW7vbUulizRg4YGzlgIsdY+D2PdZs+yjXZlFXpwaA56OO6jjaNDIwMPI4Bccn5IWOySoTxuNn9kC4OGfwMetSvbgZtPxpf7OiK4CecmiZD5EPkOg6aowt2l8wGSEKd2rmgfjlEDiqnYVAOMjmWNgd3g0wHrLQyQDlMCljRclABBdUAW2ki39LlQZNtVjtRXK6psWdxsGGb4u274zVx0GTGDzaMA9Y2eMW3vYhatjy47ppQRbXJm8yUibYCcQ8147ZbK7i76BoY001ukb+3mlthGPWbpWQWhTnAQcFP2aLjIlH6YqkJFWMyKcnlUxy0lSwpXwFjWWmdRuT4OvX6QYGh6JQOscZFylURRbnioIqP1rJrzHM4sBlfnHGeTOYUW3i5TdXJquB8Z17qkKshehJgHV/3MDLVPDiVOXKkGloWnG/diLvXdExz1GoWRfECQ0DkMjWGYNjaHUdAIPvgB57HuwtV8XDyLWgBRL4zF+dAMHFap29nxkGwtsCOPI46xeiZylfccM08IMGSU48nPwDz5oIKFEetFAFyqbejljIMw9Juhw0CEecYVK0A0KGG7YYrOFAPbzIEsmc4ICLksQJx6ROGPoJTFOFUM8+VszlQ5JFGS21nlSTcMAwHRbuiBIiShy3gC9UwB4bTS/72u1xpDZbwyLf2VXmt35KvdNXzHDmNoc0HHrUOUC0ZhtGisJohEohcR0vgURzoMIRJELTbEBU+sOa04XIgJ6t55NjdFCgtE/cnKeUT0m2odYCWOiWGYbTa24aQzYF5vD8WSgw53yh2rT35PgWbPBw0Hz4qhB4/AK00D/3CyDl+gPnAS60NyNpBAjAs7X4Olh/vshzggHaZitwJUgH52DIH4mzWZNJK7TYYe5IuMw9utnIOB2ReZCyEYdjaKRtZgGQ+WH58DAe0yQhqN1Oix9Kd9NFF5US6XykSS6iqxNWM/l4gEWae1KPkNGeo4uorXBafMAxstR2vVKk5CMPV3np1mVywxQnAdWD6XD5QB6nAQY2LMwhZ+CS2xsilC9ZycEfkPAE/oN9hQNmwfYFZAEQm4At6niunOYCMCcUElAmTX5mrtotSeVgIhoPCrg/gY5Nk8iPlpy5MDwnF5n/35jl1oj/Xdd61WihR8v9AqHNeWIHgiR3h/4ADCCb73BjmwHNujFmyzW2h2Oif3D+IoYDKyCjBHguZNN1jGx8yzV+ePjSrX/ejegz9MnnJGtp7xReefO65oSvMo2NBuTt/4s7aB+KoCYTfS4yvQ/pgdmtDczSr0A3gFQ6Ga/o8Y8MohOMOFQdD5kAvyZBjwbglNEgGnBMlDfAfLMnphgXqCGdkYGRgZOBvMvAHiEuUwSoWRLwAAAAASUVORK5CYII=)
Let sin x = t ⇒ cos x dx = dt
When x =0 then t = 0 and when x = π /2 then t = 1
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Question 32.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAAAyCAMAAACpvo3VAAAAAXNSR0IArs4c6QAAAK5QTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLyQkLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/7aQ/9uQ/9u2/9vb//+2///bpzGnewAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAFKklEQVRoQ+1a63bTMAyOu0u4DBgrjNvaDWg3YBmDhpT6/V8MWbIdO1Fsp91CfjSHM7pFsv3pLqtZtn/2EohJQH57cRujMe+LVz9SSYnOXbw3c7+t4tSbtwKfmT7b/PUqzmQoqueazQfVtYD0Fifm/yeAmx/LWVYc68PK+Vk6bqCsnizSJdZcnJgd6fXaentieS0EwnSRlwfJpk47F0doIhqUFQR7rNbixBxm2h5gJ+fyLIN/PnI5N8pP3VAfW4MqJ9oEOPb24ppZSy91y13pqqdau3KurP0vqq7K0W/lZ/J9bRTNrZZCHK0KCg2kbA0KrEiIg1v585kQp1lWAsldrj7hQ4u3mYdW+pLMNMs201lW5q/wN62z64WSixYDI+IlqFYJDC1GWYkhRX4Qw0oqEvjzySIrTPDUi7eYjavsqstEfj6UWWsNI5dz0LkOhShBw1dbO8pC/9CU+mWLWUsv8eA7k1U5F8QLE+A85GCg+jFuXOUvjQ1HkW+meiezeJMZkBv72xlWwgKlsUGPNlHnENJtKMNTG1DEL+/Pc4wCqHOL3C7eYB4YufW+rZBv3r031oF+7lm78nNj6BzyJvPQyNn8Y4OaylLdEU5eLjZTyn+kUQ85/lL7udW5SRxN5oH9HGNv67EpV5kvhII/bHqWqg4oqQzSdRhlQ8WS3XyBH+sP6i/oUjai0OJt5tofErx0ZxI554s1U2Yt4bWcTz5xG8m5mIDOKdlTFWIldi0mswzS+unvqZhVytsNobIMXLTFPGw+70K+bd2eVPXydbutgHdWZ9ICm2lHge63U7G1bLeRJjGuV2PqdlX7xXZ23/uNdaT520y7UuiW/XmaxLj+nOnV+JTbJQzaWt5Du30Yb/66kfcRdrfg01fhVNSdVdioTH2XuMjWZMnB5q/Khyyb0uVAlL2Q6xCDdYWuUkLN33iRV2C0LyEluj1dSHJe76vdJKT0UvRtxPvqbUv6Kr/I5JWKcG5PF1jMsw+VjDHJKgdotxvq3WiRUwOkkLs9XQC5exlipYCmzz88ctuTDf9BH5NKXULg9HRpyOvUGmj+xqpzF7nTEAaQ28a6LiR1C8Rbe0FV9+geF7nT0yXpfAkton4COh8rcorU5Od1TxdSUN31Y4QghQb8fKzIwcK/ZutzQO72dIgGWw2VsKn5M22yiWqYyZDJuQxhRMZfTIzA+GEKMDn9lYsLt6cLITf5XHu10zrzaJb9eoIRiKTzCEybGKrh+IuJHQCaS2haYsixSbtNDO7+yMiDs5Yd5MuyNtvE4KCu62LCX3l9KcDpIGJCLU3XM6qohksXf1KivdBpqUOzltR6vId8+vTnqjKMLq2I5BUQqlr6niYHqhNEiM2q2rf20KwlsR6PHm87ApMSgtxYVVQvVjgIwBDqFAjNqppBTh7fmrUk1uPbAYty2ZvgIOW1OPlusyOg9rjcSUlrBsNNmZzbZzugiR70wQkSW3+YiR7eQs2AyA5ufXnVkxJ1PE7nHbOWtHr8wTHTgpgDYVbMXys7m97nx/V1uIe8UVV3+Dk3cUirxx8JOab64ngVvrECF1eubW893OuPZlXNIO+YtSTW44+DHI+p5ubBy2KM5G8hsJVwuSfvIK0V6sMNDg2dMUs7q4VmLS3Ox4HIrbp5syiVyuH/8ERrfQkzEvxGAXzxYfJRfzj8il7tTEoY5DBm6Zi1tDkHRD6F73qokB1DPtyRBt4pau0Dn2fA7SB4DdlZDIgsthV8+3FyESPav99LYC+BvQRGK4F/my21Q6DjjGwAAAAASUVORK5CYII=)
Adding (1) and (2), we get
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 33.Evaluate the definite integral:![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
First solve for I1:
![](data:image/png;base64,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)
As we can see that (x-1)≥0 when 1≤x≤4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now solve for I2:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAAAzCAMAAABL5aH3AAAAAXNSR0IArs4c6QAAAIdQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOmY6OmZmOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZrbbZrb/kDoAkDo6kGYAkGaQkLbbkNv/tmYAtmY6tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2//+2///b6g6drwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACTklEQVRYR+2Y63LCIBCFF3sxvdlobRrbSk2tLRHe//kKhNyRoEVnOyPjz3jyZfewuwBwXseLQB69HE/8IGWxuMOGlCUpMiQ2EViQxAchjwB8vhJp8vZzUM4D/4k+gvxBRtS6woCU367Kb8SSOFoHZhNdVHiBU7GPnEhl0nCtPEKHxAiyWqQ2Gj6k0RKXkwAoOiSRotj3zUT1kXisa/hexUE/rMp/CF/yuBslHuuqsD8SQGveYm1AkRIy9nItj7tdzR9JfM0IuVS7w/C3R8BOeeGxHxH8BYmSBLY6ylakzowqUk+kPDo8SlS9Q9e1EyJR5XRpW4drdXp6SLlM6b2c5BsC3lFiPc+1vKSqlntkobbE5VEC4lXB1gIWJAlsVrM4DiCJVEbJ1ZcLw3SjpAceE79SIFSU5L6+n5ita/smw9JBKgJd0FYCwZAgczWc8jUOpEqgePZbmqz8RuU0S+IydRJorXZd4vNnR8eh42JUdyBVAhqJT99hPdBVB5DEYukocZm2jPymDlIRkMJLlUClk9+4Zw83klBHF9YLpImq1taPdO2djd5h+ySRaoG6oTi3S1npdiVOyoxklPQxz7KMFSxI8mg4mmwiklgE1pWVdnQ82iuD/j2ulrRWb/sbsyEiywR3XCQmiZh7hOkPlUedl5T4wFSFcqhEcQnQtJ33XOU1DwZ5yHg5iFYgEXy3k8B0AxMfnjNooEA4ZXSX+nyY4UEqB8YMCRKfLpkpAWiQ4upmEgtSw2T4kAS9xnCR24yRaoXorgdPUXDO7/iPEfgFs6dAdelXfzoAAAAASUVORK5CYII=)
As we can see that (x-2)≤0 when 1≤x≤2 and (x-2)≥0 when 2≤x≤4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now solve for I3:
![](data:image/png;base64,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)
As we can see that (x-3)≤0 when 1≤x≤3 and (x-3)≥0 when 3≤x≤4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Question 34.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using partial differentiation:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ 1 = Ax2 +Ax+ B+Bx+ Cx2
⇒ 1 = B + (A+B)x + (A+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) B = 1
(b) A + B = 0 ⇒ A = -B ⇒ A = -1
( c) A + C =0 ⇒ C = -A ⇒ C = 1
Put these values in equation (1)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ L.H.S = R.H.S
Hence proved.
Question 35.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALwAAAAzCAMAAAAacZKUAAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZmYAZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkLb/kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/7aQ/9uQ/9u2//+2///bty9rYQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADLElEQVRoQ+1YC3PTMAy2M+jqwRi0gY5nCQyabs5CQxr//3+G5FecF01bbldx1e22xbbsz59kSTZjZ/nvGVDrKdk9Zq8XdMEzJs/gn9T11JrzuV6RIPPpnMEPTfDliwdraJVebp7U5scvlk4sYslBjAmoiEpo4W3wWgrC4Av+lYqTdHFK0uCjFV3mU8LgVXLhwjw9A5AGX8U7mX8U0aoUNpUVfO8DrpMfSnsllejm6/tDbV7FLsEOz1BMNnLmCoeRoTW/9XFAwqmSFw9q3aGpiqEGz8VO+oagjQHP5LMvXr8UI/LCdhHQLCELAnhWvWufLpXgBeLwYO394W+my17W5hkDvnxzj2gD8Z/lgvNXzk8M+ILP0Rkz8E5mu9GhLjelQAqgKaq5a1UHLbdJOQcv0Z7t1H7/VMlzXBCnvgHmgzFDex4AX4ol2/oAVzNfiutlfgVHy3arBGEViB2acmftUjTuegVvX/0w8KsEsVu1TExVCjvSDeo7bsuPGbTXAPgUV/PG0+BzjAW2wqq78aAwdDgses0mteYO8Lhp1GqqoaounvWB9WOw1QUTHqa7fvBVjBOb3yA63EQYC8x+gm7cTfV2ZZt82d4kq8s8THQz8zMFamZqs4wdM0i8PqGB2E8zhSfS/9MAr1uRngL+VnFvlDVT94Bn2mRdtRC8HXMY+IB55wUd5tHfU6DJj+1zG9m9O1XvPyJtTTVvCruMGaOdaQ+3Meew6fMWFdoz7K7iTx9gbG0cHNfy+S549W2lk0dTzVvb+LwdM5p5V/5BWIRo4wKcXsc6AILHqOm7U0NrwSFKZP2xsgNe4UsCTtJVk9EPtr0F8PWYQfTG9ZyAdez3o+DcZWs8r2YfENEN1KAb4yRKJnj0uf9hoJ3eYMIImNdztdXggSea/RJ8GYzpRa/uAAwP0vKwhY7qSfeus45a7t8qU76L6FxJVUjfRUxkJSp1pCW4gU4apbSHMVeLk92PTmPqbvCucrLAEZjE8yqnm/KKXsTUN6YqhmqF2kM3XFTgUQPAw4WF6QsYIYHySwd5kuAdzyTdpq62JyQPrMFfwbPOkpC/n6GeGThdBv4Aj8RirIVvnBoAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
L.H.S = R.H.S
Hence Proved.
Question 36.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As we can see f(x) =x17 .cos4x and f(-x) = (-x)17 .cos4(-x) = -x17 .cos4x
i.e. f(x) = -f(-x)
so, it is an odd function.
It is also known that if f(x) is an odd function then,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence proved.
Question 37.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAAA5CAMAAACxth+gAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2/9vb//+2///blGIqXgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADiElEQVRoQ+1aiXKbMBCVaOPQI47dEKetjRObpHWp0xoo+v9P664uxGFGBSZBHTQZlDGSdt/eK5uQabglgXxF+di4xXaF26dDtCHxpdMYkPkJxWhUyEK0qD+n0TDUiZE82JDEXziOohP0adMkgf9UAuyR0htCROaG4SbM6IbAn+Mjff/DcQS87pipDPEb6sGlm4hYqKwpv92Ro7d3Ekbqmz6RvnMTRVJqKGJH3Tw2URwddQsSG54QuwqCRAWKBEAkTjasLHyj0kUevEbbPUh4N1C8SogdJrzngdZFVxTs27xf9i+F93hxKBhJLK9k8kCn7gYU5TDcDJOFn0Tyf77rmGvK4T39aLimDQNAujcKlfuzFe2o1Wp4N1WT+lbRJvXbdGFhZIngPV0c4m4o6uE9LljqhSLbUuotT9ws8fHTl2ViROnsFBvWykJ9D9eKIoVK0wO54jxHy5ckiAzv5sFSGbj0GnQhX7VJNKENt4EsnJ3YPUiEiyL1r/ZEpXhML3jlo4YhrDYUqb8mGdyx8BmDuyKhw7txsDBSXMrusbIQr2DWjVy1Zm1EkQdwTDrXKDgUUWEhddMbk+LANhSq/I9QZohck1DiMA/mq/gW7t1VmnWtNKIgj/TqO7d2oQt4cKrio2uzTmlEUROa2i1m/lQkDK3qgxGAWCpUXaFpi4IcP9AL8NoGFKXCixBDAS26KKMQviRJFCwVFV0VhaR53qJivDhoGs8+kGpAkX/+YsYiO4tq0AXQ5CT0MA6uoqjQrLPbiAJdgttlHQXb7vPAIG6HQkUytHAhG01C+4VxMPqF2CL8okLTFgVGkhWcwg/hD+ndDG9LEtCfgmLGqJZuN6YQcJ72fGuGUHiwQhJy6IOV34AV7Uh2B7Tlq2aTEZ+WmiS1MNv6lMK1cwrThj8wIAL/LKQe6AL+Vyi0lB9gGX379RwtyDgXO/QGWLYEfSgSCoQ+GJ2Zt81wTeYtf/l0LV+1oYj6fgMmc3cbjX99Z+Ruy61Gk2S5o7KsuEPptr++q8MNRm8UYGWyph0IRammtTtziCapd39RYrXUX9iB4MndcumIl5Vi/4j5bGdNl0fOIkDGLbuQkWPk0Z49UO9suho5AJG60bnjy1OHGD0eeLxrw++5h89dLwUyv90nqAqYoYJ19WcsUNXxZOE2CqVzty1KWy70Q057twACv1Lz1i/ljROdSQKTBAaUwF896Was03XYPQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAAdCAMAAABi1ltQAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tmZmtpBmttvbttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///bfiVZCwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAC9klEQVRYR+1Ya1fbMAyNu7JmG914hLGNphsYGJiyJF38///aJMtJ4zyqkHicHE71gfakjqyreyXZBMHBDhnwmYFsmfh0N1FfchX8uRTidKLh+Qkr//qYX1wHm9mNH3/T8ZIDd2grCCldmLiyD28O5d0DyFQZeHpN6NT5dEjwFkmJ0vaezfTKMo+EOBrWGJXVaYmSOFR+QOr75eOOCHXy0M2KjoWgWumyPBohryyEatQxKvZvYgWbAsgUi7TF+HDKl3R8BrnXz1D1c6yD7FOHT3wjj/aDhAVjUebRKkjDk4R6D2qDWlGbseEUL+nYhCXFVbCN3iGp+1qajv87yhINKJczNpzCQWqQBRKjV5Q05RRWdlyRMOu2i8sMpDID7/i5RIfbNTw4BRVJLGSoSfwRFVsYDEsOJKibSbr14KxLCWWNzLQylFm3HSizEKWyAhzwGUNidXyU6J8mnRL8YzHWUPaZH2w4FqWTPkm8GhFTQZDtYLpugYb6ig6U0srDSAb3NOtoVCBgguQEwxJpXu3HZZWochMTS8UUas0Y65ZQ1uEX2OnT/L0Vx7/LTH+macGhbGSVDcfuUEFp+xAGWZt4L0ZZ58FFSbFtPoq5rTxlxcKhbNDbF6Uikbo0IUqvim3hEnZ8Dkkz+bfvFMVQlPqWEe6OS7kojywulx66T5FzLEECY0qS9oHjqp17A1E+fbnsi9KMj5RGulOXziRhx3BH91EwjvXdTZCKc+ixsJVptiY4LWFTfG651L/E7EdDm+0PinDodF+axi6OYzELCVCRPjM9zIa2O7S65Y9UXfPyKRTza6zGEC7FkM/tGr7AAQf6GbRwLA/suTgv1SLpe9Uqw+FQFlqy7Ysa+oj73OgTHh7wdn2wJ6c1lM237Nmn+oN79um5kV02HuUFiKo+yrgYWJTNvI2hcvxpPR+AUsv33GWP7iQ723sn4ZJqBtCo++UAxeLF1HSvffaC+yUL0sMCGC+j1OQhhFdwAf/eml29wj6HLd5WBv4BU5RTsiqMQQcAAAAASUVORK5CYII=)
First solve for I1:
![](data:image/png;base64,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)
Let cos x = t ⇒ -sin x dx = dt ⇒ sinx dx = -dt
When x=0 then t= 1 and when x = π /2 then t = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put in equ. (2)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALIAAAAsCAMAAAD2OBJpAAAAAXNSR0IArs4c6QAAAJlQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOjqQOmY6OmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tmZmttvbttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2/9vb//+2///brfhGvQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACjElEQVRYR+2Ya1fiMBCGk65ovCyKy16gLFBdzIJtus3//3E7kwkgld6SivSczgfroWn65M07kwHG+ugV6LICm+/LbuGnY/7lpVPIariSHUMGfXvkU5isV9lbZXUXV81xbipHU/Y65vy+hPvMkLNvL9njgq2DktPiDJAzUBVjCsomV0ZedV2GXLaeKle1c/95BW6QhlXPCFU+FE2t5wJWd/GrnVe7z7JDtsm3LrOy+2t2T2Yjzi8r0/zoi6S1ww6Z1JV+xDrknPxVFNmocBerBVECHKxDNMa/2PoiAeIEje0a2aicmPkjZ6MpS8QwpuTDXaNcdA0dfjjyDg0M4hjqdrV/0hlZQe0KgAGvdzhhOoMP7sH1EZoffIw30RjbgKLsSAxOelP5XJGVmLAUdtxcQ2hxdXgZ698mUSOYHw2cQy4ubcV5RCUdY898iAwC5UcUeDmyVSRCX6GYZhxVMaQnvgOVnSU2D0rcUhM1Vc6vZbsQupq/T/z2j51Uia9UyKqQ89PuRX23vsbI+RkOkWnd6xs+sG6VdhurkCuEp+rSkjGOqAyv3wgqP9mPn/QFzhN5v6IW0m/rJ7QtkRkbk8OhlbDlvi3kgyLnepRIPmH6eckS/gAVA0hN6RijyjoCZ+PnVmU950GLfY77gf1X8MECHQytF1bjdAb/wBEHCQ0FCV0IzEZleRWXdpsVhm5+2/vAxvNah6h5jdCQw3ywrDGyZIg/8iMQmPJdI6JgAT7zbPJPjIxLk15dE3VeXv1yI2OYjYg+/ScuqHxN0i+dD9+0bTXM9AFD4PtqMKk7L24q1p1uxUZ8ujEaC0bHUKdCiQ4h05GTeBa5k+6PxlPEtCzdiRR/LcKWpY9egUIF/gPDmD+gUpfVdwAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
L.H.S = R.H.S
Hence Proved.
Question 38.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
First solve for I1:
![](data:image/png;base64,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)
Let tan x = t ⇒ sec2 x dx = dt
When x=0 then t= 0 and when x = π /2 then t = 1
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put in equ. (2)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
L.H.S = R.H.S
Hence Proved.
Question 39.Prove: ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPoAAAAzCAMAAACJ1eVzAAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZjqQZmYAZpCQZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6ttvbttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/7aQ/9uQ/9u2//+2///bKQaNnwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEDUlEQVRoQ+1ZC1ebMBQm3Xzgpk7LpntW1JXOoV0ZJf//n+0+QhpeFSiEnpUcD2oScvPd9704zjhGDvTIAbk47fH0fT76+cPNoUJ3nHCEvs+62end5EKIKZ14cFIPpg78HCL0+N1vpUQyOFl1qk9lh8lHoQaze8gRHCu8IV6p9/ss5sjr2L0bEjPTln7vaHMg9wZ67B4s9EjYVr29kXp4wNAnc8sOJ3qzJ24usA49JOjTv7ZZnpew9OEizcauBV4AFKU/+dGMave7m0P/bwq8xGss9cpUPxI9uExKtHDk7yl9mj5/aqsPiZcmc/kTqqNeZZXTWaBc3mpHEIIvAu8gFwURJR7U2Eu3uegU0rrQE495j0lAJfSO0tP1jSHiEDIudIzJp7xPkj62F9oH59itknq1HvUMPb56QqzG0P/GN0JcpBrO0CMxRUN7dkE71DKawskqdpGBMFXlUIvQ1/dCTK5XZLh8qLjOsEEXeIEQxyuwRUoHkewlFCWZybZmWAE9dmfOWoekjdRj93y2PJvrZemjPDl/mIFNqHw1djNdqEjkmlL4mnyAV0l74VAwtYz3Mgo8zAmkz8iBhnzAjcZkW+Sk4SVSD/Cu2qoI+hK1VtUhm2V0EA6aCpalzCJ6czv0xIM34gsNnfBXVDjIJiQAg0pfcnPGJM6nDlo0SZ3KodPVHH7CIBcP+plyw1jGGycf52qvLsuzoihI3VmI81/MI0IND02sIMXYvWRj4C0sED1ZKnTNCiGYZ2W82QZdC1H/oejyHWgW2R/Bb+Wcy4NAEbrz8l4cgb7Vge6QZuWg68lS6LUma0o91V9muakUYOdBQWg5hQ/L+jJLNIo60JPPX5mjptT1ZKVQX4VfDp29V9bW6SieMpcT79sX2LtRDN6WsfUCdDRzstwa0OX9nPKKlAbbup58FWHlhhz0tMSCQAYePo3GijQcolIpczlgkUYCvO9zeblQhI4BBD/D0Hn0qHJzEhu5SA9GOPnprG9htznZGntqR3wAuANlVy+uEOjXmNsYW1maqqdoLGNkwwGhefK9vNlaSIbW93DQFQodAjY90FeUuXigPQGp8yI08yfXf1wxMyfbQZePQFW87b2yC3qoOLYjlktIfo6GLtZRmZqE23ZSzL0VgPmtW9SLnRA3DxkA+m5FR2ccaN6p6IZ0Z+Vt++twLLQ/sEk18NjERqsX6aiw3+nO1en5Tse+8rL9j10lFxqE/dn0sk8ebzubkh747mu1NRycDuJfcnwI0cuFp6v4zF6OQTQj2x858wpALZbEg8zb3qdm4jJl+sMNaGNEKABsZzjU3LEyVG9iWOgeVz6WoVvhb00ilhW+5q3sbIPGhE03ZwdUPSoJtOln9baOu0YOjBwYOdA5B/4BWY15TN5lT40AAAAASUVORK5CYII=)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAAAZCAMAAAD0WWkBAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZmYAZpDbZrbbZrb/kDoAkDo6kGYAkGY6kNv/tmYAtmY6tpBmttvbttv/tv//25A625Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///b5WTHMAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACs0lEQVRYR+1X3XrTMAyNwkYDdLBBKbClrBkbGWvS+P2fDkv+T2NbzddxQ32RC8eWz5GOZLkozuPsgf/eA+JhwffBUYv5Zl955fOnNZ/jUYtfGTiZH1YAl7v8SS2DYwsAd2iKszh/pPh19dutaq+f4ltEDRAHOKy+eFs7hXFi8GD3VYZjGkxwrqg/S9+LlzXAxVb+6T/EsFGoEjFIccQY40DbJ+KYBuNzFDU5v4HbYr96gwHt3yHV6SFqNse4Gk7FMQnGP74jXkWD2FudAkFS9UtPvAyO+w1AebPrMGb4ea7gJhRO81YlbYPpKxPP0403pbQqzOIJl3E5But0Co0C2ZUurnmOor7ciZ/SS4Sxr5Zb4zqNEqsJqMRtpGVRB6nhpmi/t/iQJJejzmxloFExJfmaBEJEjqQzKz2uh/1L+Uif/spyJKJ+LfKwoj/a8J+bCpBNCp/L0Q+StUrC9UZbGl/n41g8wPIR9+o4yp1hLfIN99XHUMe4TU8dcDzw6gyOuvpgPEe33FEciz/v4ULqgcOxaL08MFrWU6eLY6vkSQq10UOOc7WKpl4qaYrDcfj23Z6vYdgp2i/uofwxKVSHONvuOa02C9uihHE8ruZgKpIQGBzFZju+cN2UqjmLXfwqU1HJt3uWQIv67HS98/MxuDvyPUBfyYsWO1Iq0vSJ1RzRyOM6VWO1YW8KOQ6rO1UBJ4cBM7pvRS21gdegOdeonrxFJ6RqBKOX228qgGsMo7z46IOqn4IpjZUyjuqnwutPEcevEtW4Ahq+FkyOo8lCXbQIS6rRieVG2jepXbF/WY52Y7Zv0n2OfxLJdsaI3xEzjFE+p7VqrGY5Hsp9bhgT9+Bcjli8snBS7Z4+WL073Ei+O5Jgue9HDmP9fhzWUN6m1yfbPZu7/PcjB915zdkD/9YDfwEpRU3Sw3TOtAAAAABJRU5ErkJggg==)
First solve for I1:
![](data:image/png;base64,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)
Let 1 - x2 = t ⇒ -2 x dx = dt
When x=0 then t= 1 and when x = 1 then t = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put in equ. (2)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
L.H.S = R.H.S
Hence Proved.
Question 40.Evaluate
as a limit of a sum.
Answer:Given: ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAgCAMAAACy7Q9eAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOmY6OmZmOmaQOma2OpDbZgAAZgA6ZgBmZjoAZjo6ZjpmZmYAZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkLb/kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22//b2////7Zm/7aQ/9uQ/9u2//+2///b0zS2pwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABt0lEQVRIS+1Ua1fCMAxtJiIVFIf4wiG4Ih0+qGP9/7/NpBmwF2znOI9+MF92Tpfe3NybRogfDbvotYofXYzbBRRC/1nASMIjqdcWQ9P7CKoB38cAw6xRUR+8hzrnLKMJYdXZOpecjOZi5YX7MzstHFRix+d8RQPGVTFl+3d3Tgcr6YWx7LryBlivfZgsh1JJXSixmU0IpbvWw7QdUwTUJ8vDqqxIwsQn8o6Jgg4BCt3ZSRnLAkN1BFDnLHF1X939qM8NYzQBjMdspkE8k6mfjEK+//lsg9MXBMMxGOCBAkARAKiADUoMYzlxRLjVbEM4sVQpkj2rEIIS7ZOTAo1Ix6UCUGE7NmjwDikRbUZAGyBD9q8MmPj0xyUfD05kDWM5SPWuAnSeHjOfC2UBhd5O3yGGdfQKgMntXcqAus9fbiQfq0U6s4bTMPFZ9YrrBtC8qHYJ4Hh7c7G5QUCrUE3DD9cG+LGz3Bah6biv9QSvLcAbvkmYBOAhQ57DxEfGurcubYEGIlamEBCBOqbfjuR6SWuanpRQDSa5tmAs4RK1ag8wrdhey9sW8J21Zgo/ItxXbnH+x68r8AXJKyrLlHyOowAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjQAAAA0CAMAAACqylIYAAAAAXNSR0IArs4c6QAAALpQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kLbbkNvbkNv/tmYAtmY6tmZmtpA6tpBmttvbttv/tv/btv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///b4H8WzQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAH80lEQVR4Xu1dDXvTNhC20hWabRRoyco+WAkDlnR0HYZujRP//7+1O+kknWxJllO3rov8rCE00n28enU6nRRWFPnJCGQEMgKTRKAUR5O0Oxs9JgLrTJox4Z+m7kyaaY7bqFavn16I2dtRTcjKp4bA+uCqKA8+T8Ls69erSdj5aI2sL4R4Bd7h8lR9P4XB2J6JiZD70ZJm/aqA/yZEmurl1VQi4mMlTfUDrUjrJzf1p4nM4EyacekIXFEGrJ8JcTiF1QlszaQZlTT1EpemqT2ZNKOOWDXPpBl1AKaofCOmWJrJkWZUrpWZNKPiP0nl5Wwiua+Dbo40o5JtPU3STNLqUQd6QOX1ciKVGeZz/WEuhPju9wFhyKL6IDBF0sT8qy+f29Oz8uVVAhZOl472aRITlBZJWpMaaW1t29zflIOdvewWrUhTf5BnUWH4NyIteUYJqZZy/0rRY/HZLYTA8qSyul6eUqlSQlk9i2wNtZ9uF9+AM4OiEpPIQuh2awWfUhpZpWRb29oSAjMAMVgiuFvogrBWXi+PijIOf9o2XbmcaikfjQ2SJk1JsVvIOpOyulWpjBzAGj8T6lTSIPXc8ki3j9bkuqs+8yfbPNZW87sljZQPg9DAkoOlmnQ8JCGVNHw09iCNMmnTCpslnxP1ktlNTrS7SL+cpgUbhiIsMQDI/lrT0k125q9s81g7LGmqeTPSqBkehT+JNCQhmTRsNLjXXdykSCOtxmnceJzA4Ayf8tPTpYM0YYkppOmhNWRa00N25q9s4/CRtUSafz6Imdw/VGf2Dd68q7/+KMQJhneIqdUcodm+E2J2AiQ0bY3iFmk2uDN5SwavMV+AFRHh1erPhHgB05p/5ENLu1weGEu9zchaq4C8lokTvnyZgzfyxfso0iirNZk1BJIULGJy0qgeAJAKPqyLlzR/0qWjiMQQvffVqkOhxiA8fczEVN5uZi1rFWlmsDGQxdxqfl5c46/wzXaBw31Ty+KLLNshs+slXHp4DxHFtLX6N63vIMi5oLFEQeS0MghF1O+xCfvI546WYC0NUIus5aMhp4oUUM2PV+Dn8UfljefhkYammIUA2vObz55I4+siScRXMkDx+EqBGpMYGNV9teqAQRgocnsfG82ltx5riTTgwG4BTfBmg5zV5oqDHFpQYTIDiWv1/Ma27SSNNhj5BlmxBUtqobXAfoRxhx49tlqCHGxpafAxDNWNOGkkc9D+QB7lIY1UZISy5Tc8fE4XH2kQT9ozcqBdbvk93FerJY3GIIE0Znhca1lOA+YrzMwbEuuSprgQx3/DJ6YtUx6INGZZrOYv9LqAYCkRakDYRx5vDGlkNkdAt7nlHd8WaSRqqBMfw0+Bf+Ok4flTkzQt1QpVbxf/DOiUWOK1/Gp+inHqUFWLbqNVmyb1kpseiY4Tak6bQG2Qb5JGenjw2Uitr1/Dco0zw25cIXEAL7CkIdt2k8ZiaZeFJmmCK4YUryWoP/nsdBhmrOWN4qRxGeqLNF6h0C0y53kXVODZPXXGLg9pWqJom0HxOKrViTRmeF3v1d/Y8pRIGlo8tFRc0BvLE8q9nh9ZtjLFpbxTzh/plok0u59/0SRrkoZ9FFueoqSx1g5IGlcoWxjj2YWzAsZIE5LoG88oVR1D2/wiZrmRpoM0MqdxIo20luc0WIMjF/Qb28NEGkxncK779nAdpKnfrUw+gkmWEqFyGvaRx5NGThOooHn8c7ymbBjUpeQ0er/BQHNmqIc0ni7SmTBpwhLTSZOkVXvcgzS0lWz7r0gjYI/0Sa0/sJ35ApvvEt/8tcKscfur2nmc3Gxfy20l7KvOYLR1W8aeAGnI4Bq/prBRwUgZVM4+FlIo/8iHltk9GUv9rbS1bNlWpLQvlAj7eeep01gIGgXccJ2Gd/GRxhgUk5hOGhqAuFYTBtR2NlK4NikE1Wna1irSnMIRhroFDiWM2RssBMKbw48FZL3i5L8F9oMvTL75Fwo123eQ5LykJtjWIQ005A+URuQuHSNKvYRaD2ZCMvuVhSP4ktTsBISe8498aJk6jbXU18xaa0vCYMIMyC8LL86LTwBNLnW6QgVFJjRYv1V++rq0SWMNwmkTrDEnkKaPVvJGYqAHwaOCn/lL23zWhuJ0wGQ/0IYp68DZY0dBPkFZoD4f7umMRoIC1aSxWkQOP/wikw94qPstz55ISpLWpEbcq7Zt+jcDkObi3KjSFasmon2O/kYdDXdb0eeU24yfczDewdZbn3L30brfKTfzwFg7AGmY2BBpel0yCLHmPkajsRfN92nYYNj7JoOSJnIHaw/4G+Tpc4Wox+0mcyBFy5O6T5OfyMJP+dtAGOExwUCi7k9M92HM/dnyLWqKHwqNgshGPLmc238n5wvu2XZnUNGGI/pDeX2TijcJl6dGceDRK41Wp0fyHktB7NgBs3b42f6Gx/lYplSkeYiWjwTYfasdNEEayHjcesMPljTkM1vVf8D5VYkFaXyTSTMQ0PuK6V1M2VdRj35EGt2DIs3XZ8dXOdL0gPHumu5XULs7e1CySxqZ08A12MMVvticJi9PdzsKYenqMGarvlXxQB4omx/BT8Qgulv4cEx+IMjdhxm7n1Yb3HDvFufFxYR23l2HMfeB3TerAw7BDFUke/KTEUhG4Cv8u2mZNMlw5YaAAF6EKulOawYkI5CEwG4pDi/z/00jCavcKCOQEcgIZAQyAhmBjEBGYFQE/gdzOF5gB43S+wAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Here, a=0, b=1, and f(x)=e2-3x and h = 1/n
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 41.Choose the correct answers
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put ex= t ⇒ ex dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, correct option is (A).
Question 42.Choose the correct answers
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Put sin x + cos x= t ⇒ cos x – sin x = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, correct option is (B).
Question 43.Choose the correct answers
If f (a + b – x) = f (x), then
is equal to
A. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAABDCAYAAACRMJdAAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAgrSURBVHja7Z1Nb9NIGIDH7RWW6wKZ3Fg40kzyD1jHFQWJQ9Q6Vk5lLRRF1i4p8gHRtLdKaDnvxwHKBZb7Xmh72gtd7kgL5AdA+QmE7LxjT+I4TuKvfL+HV2pTxWPPPH6/Z0r29/cJCso4BCcBBeFCQbim+zCErHBRcGERrlTFtkuXc4T+q1mNNVxYhCs1aTQqFxkhHwihXxAuhGssgIHmulF9mOOmcdWRNppIhCs9uFRdvZsl5BOHq0XV2g76YAhXWqaxSej6a/Pg4Nxehd1UCD0DTYYLjXBBtKe4Jk2JA5fXoT84MM9pGXLMtVcdF3rJ4bLN0ne6yuqUkC/M2NtIChdImZFDhGvJ4QItU6TkNVdbLa612mnAZdvm+WJGOWaVvZu40GgWSU2l9SRwMUJPuY/FwLQ2dHaL0KLwv3ChFxCutvChwqcDksAFUtXoff79r0IQrNmF65VTSllNkjMCWKL4PF642l3nnsurFVysBYELnOsfWfZPqQUgpM8UN/ejRnFx4SroNd3Q6C7kqzhh32hu60nJtL/DBZtzuGQITwhr6lbjCnwGCx3HXMWFi9L1lzA23AuMDYCRXPk5JkQXAC6I3KTPAgv6SF+7LRY9YlifxCz2wE7JUdS6Iekxq1gGmimfCxbHNEsXanpBp4R8HgVXr4/kyD2VPqDqvQf+zwdpoEEOfVRHH65f01kZcmbufWMZaFbgAmfeXZzPlJUfWyq7Owqunkit46tB3kpp+T8flHsaBNGewTaiaE6RhuBjy7wZ13pn2C0xA3DBG17O0SdiQep71+Msbppm0Tt+WM0F9w8w1bTCNgQF2bz6G6YlZgCuhqWtCXPCjGdxNUfacPHPd8Jqn6AyEMqMwOUBacdnZiL7LrHh0hu3OmkRt4wjux1GwiVeDvofwjWLcNW1644Dn2uWbPvyw2rph3w2+zek2iEdYFn6mkxRpA2XZRQ2wVcimeLxHbN+DQIKQ6MNQtiHSqNxMcw1oprQ/shyeFeGv+qQpJNjUuIGW0rE+VhJGmUHQ+H6KoRkPxW02rZjash78bthbYa9ODj5VKvej3JDvxjaOqPkjXT+IaCI4i9FhastIsuCLhsMIeXB9Fo5aDEg0IHgpqBZ20KrJuzkmJRYfD0hMR2m0gHzUd1UN3KUvE3aUbJwqjiqfyj8OaodiQbDjtbuz6kBSOuUvpSwp9HJMSnp3Cu3CKMqHW7U34rjYy88XJ0sv8dnHCS2XbnENXLTO4nQwZol2XcyUpZv8xaPQIO0cNJi+ySlzMjTFaYfjjJ3cQO4pYGLsPJhWlrOq93mGS5Z7Rj14iFcCeCSTni3rCWrCKXVYO2mNMMkfifVyVHqq3g4mqgUIihxwMk1K7Z9yTcnsgtmxQ9X3PEWF66MdjwoEADfquvAC6vnVhFy7/1RqZNjY81B0eqkOznkHk1RzHfu/RuY6+7eTQUqEp+9Zr0/VUPOvNrLrpauMqqcOn1w7I1hsJ8kXEnGW0S4dkbBFVb9dzpEhlxrGp0cMAb4T2KMjHpi2vZ5AY7IR7IPw1JF/mdqiJ3qSpNqxq743dKv8Gj91DsvccdbOLhgU0ZacHW2qw0xsWl2ckQFbN2JVttr+qPbphvNDtJY/XPEhGks58hzvz/pCYrqScZDuIbB1SmFRYNrlKMf1EEyWAZHdl3TlGvm8/Rl2M0ozhxx8A1tG57P//yD5iXqeH5Hd3VeZNbhGnbtoA6SQTIqCe2O45qrg/NR4FJV9ijoHofde5Tx/HB9nReZF7jGmaIAfw78HkrpPyKICFn7DYBrJ8y8RB1v4cyiwcizaftc3cBivH1kD6s3cjyQeGHtWd+DPwTAwNa60D5XpbAta8YD5mUnyXhLmYrowOPp9hiWdOTXOhkVLSbp5IgjcB5ZnuZfyBSJW7o6kw0HI6NF7sRbDR4ZEvLR/x05LyS39Vzm6+KMt5RwyRbuLYiU3EksmeaFoMSnxf0jxXlDAw80SaOTIzJYPFJTM+TESf46Dj8ECdBW7jy7elKq2leDTJZMClPNui/9P1Efhe/wOYAuGC2f/d3JafHPafG1ZZuX4oy3lBl6TxK115dj5acDTOPHYSWTpJ0cMSLip36Hvz9IyH4KShO4uamPXvC7XTDkK3TtOi8MdMQYP8NzxB1vKeGKKuLtDtFRMOty4JrrqG1QsQMOhCu8tnA6CuZz97fYdCMK8JM75mB8F+49DmBipyzLSCdtuLr7ObUjWf6YF4EAo8zor5RqLya5UWUsuRcohEIno+sUtgnNvVU3qxuTAKwLV3eDSZoC/gh0586VNodO1Cnc8zhyL9y3Vc58+xdFRR1qUuN+IJn4xEPfpi/pOowiL6QcUU3fleoXquxuO/C3Ya0rCBfCNdwk8RA/SP12DzcZ/znxMnUwD52hCFd60dahP7+SZiQkuz8d7Un/wn2LSwJXR3MFJClTAVccP0Da0P1ZsSuXi1n2x7jNL8qMwCUKnoSdjmPBpRnsRKZEaU0qSYgyZbhgtSHHMs5Tlf2beHFhlwAucU4WbOlHTYJwpQ0WFElRkyBcqYMFfhZj+m7A3/BkZoQrPliw2RQiN3/fe928c40x7TEexIZwxfOxPGeRBolsUkNBuCKJ25U5ZGNFcAMbCsI189L7Xz/wv24gXClJZ1OEoyVb/h0tKAhXbIFztWSXpdPTNf4ODJQlMosgbScNwvDQXYQr1UgVfC23h741ifYelCWByymOK2fi7Cg8LhzhSlNg86qzQ5isSrMYZms7CsI12qH3bnTNZt85P/efFIiCcKEgXCgoCBfKFOR/eACGxEwLPNsAAAAASUVORK5CYII=)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANIAAAA0CAMAAADIWpbvAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv/btv//25A627Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bNJHh8wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADVElEQVRoQ+1a+1/TMBBPypCqKA6q+JhVXAdoUNeu+f//NS+PNtckbboXjLh8+Im7XO977wsQcjz/gwUYPYsOZnGE9Ax8WrxY0OTrM1B0vIrFyT1hJ7/GXzhcTr6g9ArUE7lUvZwfrqLjNSuuCPzEBKl6pWOtOF3y2ygCD5AojxbnlE5iiDuei6CL6lRpdJBKGlcrgnhjEUJKYqgInVpQRAeJ51F0IuylCCHVmcdL/O5tYHpltLnG3t0jE/EbOS92BHQ5CCnpNhWJ5zSwq9ZZMzwYxXh+qQeK/g5sRvbq3HQBnp8RdkUsAZhDSAz2jUG16yywqnog9cwTPMcNDG0haHqvUsHjCLDme8U1dIbUFmYbPFXqeKn0F4xeSIS1IpT9XQGGQygThmSpXb1Bwb0BpOYKf3hN6RSHY9dLP29o8kWSWyeUKYU80QIKSk+XTOWNcVP1gdIL8BKmuja31S5RpwlCKp1c0zaEm0uOm5blpQTKgp48TKBJLzVOEJf1pZajSmeEfxdciNoHqc7AQvoYTAYSmMWhylS1IxNbBIeIDQmGjibk27clCakRwHPwkp6JGw65yUguTHUwuZ5g7avIBl7yQXLtocqD3rXalasDCdx10QSu5qgzAVEZClNtc+8YUlPL+O9rSA1coN2K54VkiiFrw8UDiRhqj5c2DDwmX1Lw0V4SudSpTb6KN+yl+uOnpnh6ICFqMPDWKg+9kKSUYC4pe/Tk0rd52180hwoolUuIGoLUKeLBVutC0jDEtrv6jJqi5SUKBfFWBZbKEHFwxePi2alUQdBysOQHWV0DJEx1K96A2uGByN0Am9SE173p38wkkwXpEqY5/fhi+pJoS1DLhCvg0wl4ST0RthzwZphM/6R0hqkeJ4XmONcK5jeFO0L2TA/9UrqzQXh6GNJnBzTPBrjum5HzQhua8Xag9qCXPEvtmEncyLTnbBl0nVHew7FHVP4NMLwvGZXsbUhSBvelPcKR34ahZc+feGzxwSL/2Apt/z3TUraXdSASwtvYgSg6Xo21e9B40U/FaXfJp9Jjd99VQ85KvVRFcOr381KU8DqbkUUctRxmSvO0EwekNtAe4C+acUESyx6bRPH/Do2X6pxO7iL8n6gIyt0RwtECO7HAP4ZgY943Ex2zAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAA0CAMAAAAEw6wEAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNv/tmYAtmY6tpA6tpBmttv/tv/btv//25A627Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bNJHh8wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADYElEQVRoQ+1aa1vTMBROynBVURxU8TKruAzQgK5d8///mif3NEkXyiZbfNaHT+QkOe95zzWA0PH7nyxA8TR3OOSIYO8UkhdLXHzduxpbKEBO7hA9+bXFCfvaypYYX8LlPA7al4t9qbHFveQSwU/GCNpXynHI6Yrd5OhFoLgkkJxhPMnQiVjNPSjnry1zR9DgrEsAOA/NH0GRYfD2wpbkjoDVOVYAl4P8EXRVhAN2+zbR4FGst9F3d45F2LXosXoH9CUQanA6ebCHD7K8shonJq+u0iXZ6sHqC1WmhwudbWLbM5uOWT1F9BKu7R3gSvATH5HACZ6jtTBuVyUGrwiCgSrNardwOG2408+2JZcJDvA6Xim18RPzokj03Cgbv7YMOGjisT2IAFFzhLRueICV4MrEEbRvXHc0XD0Bgd7C7l9jPHN9q8/Bz2tcfBHLxsRNicHH1QEE49MVlT5vSWjBv8+BA73qmLfx8zrhpkwiaII4URaCnSvmFguPgwIiWNVz6zWCA21ivlltMhJtOUfsO5fSq10FqNXXh6BdUnsRgI7JhQhcU7h8+wggUegoM68cAoE+gNXAgWobtYRo5YWUu6qJoO6YrlA/gYMYghC+jGQ1W5gRo4cAyDjXXqgkuoojknZxVmMIjDOnIjnkQGcZ9nAFbu1myjAXRRHYNEWNW0QQILk65EVkKjO65WDAi6gY8t1PccDjoJc1YrloMwfdx086rUUQOKvy+l4ki+zV8OKY4mAQgTgvGQcS/kAcfFuYcqQkpDoyDpxVmdHcbCqSF+MPEMmKFiJQWvPZbf3ZqT0eBxhS1Y30EundwoxOLhL3N5JiI0GLH2h9BVLuqucEwiYy6/DynuoqwgFH0wavSLM/lQ0ED8EFdEDqXcDWA14OFO9wdQEcyKcoIwFvU8Xsd4nnejWi/chfkbDLGqjJwwf3K266Jo9UMSEeGXDGvl4E73ypvuifI/Bby8SFfucJ4onedKcI4gNOej6wSvjdv1jZOB/sFICo7bs98blPS2bb51Zo9H02lY/eeiAbHjEuHYimQ2qMzv0Hh8cvRgenYEoh2Sms5RNJfl/3ftHwXNpVc7TMMqlC22UfGbJEYLzmHv78lDUCPsvQSY5/R9YcdDWe3Ob/byH5JaKjxkcLaAv8BSd7ZL0liFWpAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Hence, correct option is (D).
Question 44.Choose the correct answers
The value of ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMQAAAA7CAYAAAAkYiWnAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAmlSURBVHja7Z29bxNJFMDHjpSGA0oOyPhEwQEd2XFEg0TDbTYQkCisxF5ZSMBZyIpWBw7aAhEnXaRAargrIDQk6a8hUF3DR38nCOloIPwJhNy+2R17vVl7vWvvzK4zxZOIYzKzs/ObeV/zBi0sLCApUqTYIgdBihQJhBQpEohoA4RQBkSOxf4YX/lSOsg6QllD1y5pmn6jsrj4kxyT/sriYuUnXdNuaLpxCaH1rAQiwWJWCod0gh+O6caUHI94xdDHpjDRHxYq5iEJREJhKBH8iJTnL3NQGbKWDDmSTZp6xlQau3+7sfVtvkwuY1J6FGcbEoiIEwBgwFr1btztmNXCKQWj99a/d6lg5b06VZ1MChTQj2q1QFSVzGGMPmB1phZne1UN37XamBX5/L2uHEODZnDWi+QKxhOrcdsM96sXCUaZbWv8vjOxBvQHgDFafHA1CWMBqzbK5f7N5dB/0K+4gQCbYgLjVVKsX0kVEACB/ULxB82ojw6MqmRWDo5jvKbV5s/G/eI1nNnAWnGOgVc3iifHMXppQ0G2yvX60aSMy7xOJnkAQduqaWcxHl+rmObB1ABBVw66quFvgwQE7A6I6M94vPQxbeamLygj6JV3XAtNG2PIrct7Ps8MAhAgOkHPRO0S0SdPvXxUQfjdoADBJiMPQ7qTlAhasXaIT2yHgHEmCG0ydcqa9z/AvmGfWz9bn+Gvce5qvIGgC+6I9kqEq1sCwZ7H0EYxUt6JVFUaOwQpPfV+boHylEIxor5m6gTd0RDZLBr1k4OiMomeW2GM5xa328ABwUldCjC0FYzIWz8obYOT2hjU6K5UCofAAI3b3hEBhEi1KRCGmSIpYYS+OQPScImlDYggrxioKkSfnxTVv13H3dtJZWuqScpWPo9Xu1HvdlsWtCDxjwGIAIK2SUoriQLC3pLRjjWiO7b+ircZAGkCIsgrZnt98JqoZ6ELj4pr3cQ+nMnpqE6LgZ4Y8O27XbudpF37IoCgKizW1njbEZ0NPAUvwySZ0cZu5hD6ksurjxtuwhQBEeQVs59F2RBhPwAMsPD4eZ3afRdj/A/YE7yCWEKAEPROIhk2NMpqFo5bv39/sXqfpCE41+l5hA2+vXMphBTnfH6X9bUx8MQLY974GewJABzGXwLBAwjqdfFXMcCPDjsG22pFuyp7BkLA9gwwPCiOXsXK9LJXl69Vrp0mRFty9wcWoDzOv2AThAawENoGe6Jgmsc5ATHLa3xEqbGBgyDS0BxUILzOCj/BmtHQ5yHZUB1Br7F6+x4zfMFYvq3ie/T7lj1RqJqn+r1TM0cEgEvbUaafx53kFwUIp5/ZfvQr9UCst2aLeqSZY58kICDdubOBm/vidqdCDMJr+O41llv/T192Bo8mEGR8iwACFobqlDoJSZL9UOli1RttcuNdTdyTZY+4AlxdALEuDwElRxwg1oOAcBaGnX7ZOG1/AW7AXvVGajCqxq3Eq0zXT18bHj4D6RJH5GRMjIp75Mzw8KfT1+vXeBr9gUBEDY7AVjatoOc8PROddqpOXjEJhAQiViBAr2cGn20Iturze/X+VrXKHVVuGkytf6MXXdjrFXOA2JRAJA6IzXZAuE4aZv2AiJohHAxEyKxDR/d7gRrR7cyOW58Hj8lvJPdX81AM3h4Zn1pgnYPfF1VSgxNakMsCh/wJRm8gWg4uyjjy5EVFRaVEM6rhpCHBmbd0DmHyRtfJ724geskQ7gTEbBQgOm1jzXx/ssUyNHUNz7m9WU5WJ4Upl9eeaPqdCeqZsY2nWLxeEoj0AFGnqm9mC2s6PVwFB6usBfOt31yLkiHcyXuzEgcQcCoM4fGX8DdZcMr7PbY7uSe/HShE3+IIDkkg0gEEPe9u2aUIaxvud+VyANW8fyNshjBXINwPZnXu8ExxrGhN8q9hgIgjA1ICkQ4gXItirdu5FjZDmDsQYFA7UdqvmJSWDJXcShsQ3adTS2knUYBoN6eCvExhMoS5AmFveXiZppE725bf91IAxHcpvUmPQMyG0UbCZAi37RCcWOo3EM1J3TyZlkYgpIhRmSCNP0NzqkrP28y1PfZl2Azhvrtd23USqPTruHMIqeU0HvNwSSDSKa3HjqPFjnxtCNse+OTN8GVzyE4+bLYXJUM4PiBY41YnwbqHoraGoZ23jWi7Q/erhV/zudzfjPpqtaBA1iZEuJtBvV1wGje8UTSzs881QCUQ/YXBmaDfaSyKTtLw+Wzt3K6Qu0Td8nQeVA7DHNLyuSdOlvAO82BGzRAOBqKHFblE8BILnjC/Lzt9B9mZcErMzjFCH+nP5fJN6pb1ZFbuyex0HrrPQMjkvn6NJSktuRfFKK7yTsl9zTmEvsMpTjt7GOaT/gd7h1EzhGMFIjUvUeYy9U2Mcvn8nhhBBC0jTC5TX3e4sECs95hXJIHYX0LtRk8gLZVAMAPYDQToZVCTlOYgWQ+ZhHr+EohkS7fVRFIEhO0itcvEoxV2tJHmFg2IOhUVCF53J6RVTLN8LJ/THkexzRIHhDdM7i312KiKYJrH9iMQvO9OSJuAR0cnZC5q1YzEA0F3DJdx1CgOPABFCKIAwfvuhDQJK7zG8oaiXKyYPCCcIAib8NTIdqlI+x0Ir2oZBohdDmfNRe4MtLxO42CYXbUjbKmiRADh9iB5AyMDDYRx7sIBhD9P1usneABBDc0Q3xd5P0TYtv1LZyofw6pO9frkCYwOfD5n1C8IA8JOvLNerjK9XDbLx8dz5M9G2LudypSCImVdrEaRq8TFDYTI+yFEty20cl8zT4QVy8rsuN1ldtTRMqodI7pT6fa0SS9V4njsECLvhxDVtp2UJ7jYsTetwvtlGBisViHxbqiq/jLLo2AVL4l6HwEPINjEFHU/hIi2aYKngPs6Qg9MI9fIc8tN2iXqfQRBQPjdzwAJZm6js1s7QNT9EFHb7kVE3dch3YQNwxoS/MLffhkEhJ+RaRdRcKqRuKSbSSbifoiobUcVCOgl9kqt/SK2HYE2wqpNvFQm+rIE3Q/Bu21qn0TIf5JA9FttKpPLWUttCvOieQIh6n4Inm3bKULZFVHeSwnCHuMRr1ovWokAxGycQIi8H4Jn2w54q6LOpkgQfHYJ6u4Lqs7Qw90JYYEQdT8E77YXzcpBcH+LjG1JCHw9HHgJJmynl9zL3Qlg6IZxWYu6H4Jn242LJ53TdhKIhKlOAAUY2Gm4Py/tYt+oNFYEGEQf45UvJACKMd2YllDEC4Ohj00nAQYJRBdyR9cmNE2/IQsQxLPoQDUWVtA6EYDKFyNFigRCihQJhBQpQfI/NRUEcJ2JWMoAAAAASUVORK5CYII=)
A. 1
B. 0
C. –1
D. ![](data:image/png;base64,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)
Answer:Given: ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Adding (1) and (2), we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Hence, correct option is (B).
Answer:
Given:
Let
Using partial differentiation:
let
⇒ 1 = A – Ax2 + Bx – Bx2 + Cx + Cx2
⇒ 1 = A + (B+C)x + (-A-B+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) A = 1
(b) B+C = 0 ⇒ B = -C
(c) -A –B +C =0
⇒ -1 – (-C) +C = 0
⇒ 2C = 1 ⇒ C = 1/2
So, B = -1/2
Put these values in equation (1)
Question 2.
Integrate the function:
Answer:
Given:
let
Multiply and divide by,
Question 3.
Integrate the function:
Answer:
Given:
let
put
Question 4.
Integrate the function:
Answer:
Given:
let
Multiply and divide by x-3, we get
Question 5.
Integrate the function:
Answer:
Given:
or we can write it as,
Let x = t6⇒ dx = 6t5dt
After division we get,
Question 6.
Integrate the function:
Answer:
Given:
Using partial differentiation:
let
⇒5x=A(x2+9)+(Bx+C)(x+1)
⇒ 5x = Ax2 +9A+ Bx2 +Bx+ Cx + C
⇒ 5x = 9A + C + (B+C)x + (A+B)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) 9A + C = 0 ⇒ C = -9A
(b) B+C = 5 ⇒ B = 5-C ⇒ B = 5-(-9A) ⇒ B = 5 + 9A
( c) A + B =0 ⇒ A = -B ⇒ A = -(5 + 9A) ⇒ 10A = -5 ⇒ A = -1/2
and C = 9/2 and B = 1/2
Put these values in equation (1)
Put x2 = t ⇒ 2xdx = dt
Put the value in equ. (2)
Question 7.
Integrate the function:
Answer:
Given:
Let x – a = t ⇒ x = t + a ⇒ dx = dt
As,{ sin (A+B) = sin A cos B + cos A sin B}
Question 8.
Integrate the function:
Answer:
Given:
Question 9.
Integrate the function:
Answer:
Given:
Put sin x = t ⇒ cos x dx = dt
Question 10.
Integrate the function:
Answer:
Given:
Question 11.
Integrate the function:
Answer:
Given:
Multiply and divide by sin (a-b), we get
As,{ sin (A-B) = sin A cos B - cos A sin B}
Question 12.
Integrate the function:
Answer:
Given:
Now, let x4 = t ⇒ 4x3 dx = dt
And x3 dx = dt/4
Question 13.
Integrate the function:
Answer:
Given:
Let ex = t ⇒ ex dx = dt
Question 14.
Integrate the function:
Answer:
Given:
Using partial differentiation:
⇒1 = (Ax + B)(x2 + 4)+(Cx + D)(x2 + 1)
⇒ 1 = Ax3 +4Ax+ Bx2 + 4B+ Cx3 + Cx + Dx2 + D
⇒ 1 = (A+C)x3 +(B+D)x2 +(4A+C)x + (4B+D)
Equating the coefficients of x, x2, x3 and constant value. We get:
(a) A + C = 0 ⇒ C = -A
(b) B + D = 0 ⇒ B = -D
( c) 4A + C =0 ⇒ 4A = -C ⇒ 4A = A ⇒ 3A = 0 ⇒ A = 0 ⇒ C = 0
( d) 4B + D = 1 ⇒ 4B – B = 1 ⇒ B = 1/3 ⇒ D = -1/3
Put these values in equation (1)
Question 15.
Integrate the function:
Answer:
Given:
Let
Let cos x = t ⇒ -sin x dx = dt ⇒ sin x dx = dt
Question 16.
Integrate the function:
Answer:
Given:
Let
Let x4 = t ⇒ 4x3 dx = dt ⇒ x3 dx = dt/4
Question 17.
Integrate the function:
Answer:
Given: f’ (ax + b)[f(ax + b)]n
Let f(ax +b) = t ⇒ a .f’ (ax + b)dx = dt
Question 18.
Integrate the function:
Answer:
Given:
As,{ sin (A+B) = sin A cos B + cos A sin B}
Question 19.
Integrate the function:
Answer:
Given:
let
As we know,
Now, first solve for I1:
because,
Put it in equ. (2)
Question 20.
Integrate the function:
Answer:
Given:
let
Let x= cos2θ ⇒ dx = -2sinθ cosθ dθ
Question 21.
Integrate the function:
Answer:
Given:
Now let tan x = f(x)
⇒ f’(x) = sec2x dx
Question 22.
Integrate the function:
Answer:
Given:
Let
Using partial differentiation:
let
⇒ x2 + x + 1 = Ax2 + 3Ax + 2A + Bx +2B + Cx2 + 2Cx + C
⇒ x2 + x + 1 = (2A+2B+C) + (3A+B+2C)x + (A+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) A + C = 1
(b) 3A + B + 2C = 1
( c) 2A+2B+C =1
After solving we get:
A=-2, B=1 and C=3
Question 23.
Integrate the function:
Answer:
Given:
Let x= cosθ ⇒ dx = -sin θ d θ
Question 24.
Integrate:
Answer:
Given:
Question 25.
Evaluate the definite integral:
Answer:
Given:
Question 26.
Evaluate the definite integral:
Answer:
Given:
Now let tan2x = t ⇒ 2 tan x sec2x dx = dt
And when x=0 then t=0 and when x=π /4 then t=1
Question 27.
Evaluate the definite integral:
Answer:
Given:
First solve for I1:
Let 2 tan x = t ⇒ 2 sec2x dx dt
When x = 0 then t = 0 and when x = π /2 then t = ∞
Put this value in equ.(2)
Question 28.
Evaluate the definite integral:
Answer:
Given:
Now let sin x – cos x = t ⇒( cos x + sin x )dx = dt
i.e. f(x) = f(-x)
so, f(x) is an even function.
It is also known that if f(x) is an even function then,
Question 29.
Evaluate the definite integral:
Answer:
Given:
Question 30.
Evaluate the definite integral:
Answer:
Let
Also, let sinx – cosx = t
Differentiating both sides, we get,
(cosx + sinx) dx = dt
When x = 0, t = -1
And when , t = 0
Now,
(sinx – cosx)2 = t2
1 – 2 sinx.cosx = t2
Sin2x = 1 – t2
Putting all the values, we get the integral,
Question 31.
Evaluate the definite integral:
Answer:
Given:
Let sin x = t ⇒ cos x dx = dt
When x =0 then t = 0 and when x = π /2 then t = 1
Question 32.
Evaluate the definite integral:
Answer:
Given:
Adding (1) and (2), we get
Question 33.
Evaluate the definite integral:
Answer:
Given:
First solve for I1:
As we can see that (x-1)≥0 when 1≤x≤4
Now solve for I2:
As we can see that (x-2)≤0 when 1≤x≤2 and (x-2)≥0 when 2≤x≤4
Now solve for I3:
As we can see that (x-3)≤0 when 1≤x≤3 and (x-3)≥0 when 3≤x≤4
Question 34.
Prove:
Answer:
Given:
Using partial differentiation:
⇒ 1 = Ax2 +Ax+ B+Bx+ Cx2
⇒ 1 = B + (A+B)x + (A+C)x2
Equating the coefficients of x, x2 and constant value. We get:
(a) B = 1
(b) A + B = 0 ⇒ A = -B ⇒ A = -1
( c) A + C =0 ⇒ C = -A ⇒ C = 1
Put these values in equation (1)
⇒ L.H.S = R.H.S
Hence proved.
Question 35.
Prove:
Answer:
Given:
L.H.S = R.H.S
Hence Proved.
Question 36.
Prove:
Answer:
Given:
As we can see f(x) =x17 .cos4x and f(-x) = (-x)17 .cos4(-x) = -x17 .cos4x
i.e. f(x) = -f(-x)
so, it is an odd function.
It is also known that if f(x) is an odd function then,
Hence proved.
Question 37.
Prove:
Answer:
Given:
First solve for I1:
Let cos x = t ⇒ -sin x dx = dt ⇒ sinx dx = -dt
When x=0 then t= 1 and when x = π /2 then t = 0
Put in equ. (2)
L.H.S = R.H.S
Hence Proved.
Question 38.
Prove:
Answer:
Given:
First solve for I1:
Let tan x = t ⇒ sec2 x dx = dt
When x=0 then t= 0 and when x = π /2 then t = 1
Put in equ. (2)
L.H.S = R.H.S
Hence Proved.
Question 39.
Prove:
Answer:
Given:
First solve for I1:
Let 1 - x2 = t ⇒ -2 x dx = dt
When x=0 then t= 1 and when x = 1 then t = 0
Put in equ. (2)
L.H.S = R.H.S
Hence Proved.
Question 40.
Evaluate as a limit of a sum.
Answer:
Given:
Here, a=0, b=1, and f(x)=e2-3x and h = 1/n
Question 41.
Choose the correct answers is equal to
A.
B.
C.
D.
Answer:
Given:
Put ex= t ⇒ ex dx = dt
Hence, correct option is (A).
Question 42.
Choose the correct answers is equal to
A.
B.
C.
D.
Answer:
Given:
Put sin x + cos x= t ⇒ cos x – sin x = dt
Hence, correct option is (B).
Question 43.
Choose the correct answers
If f (a + b – x) = f (x), then is equal to
A.
B.
C.
D.
Answer:
Given:
Hence, correct option is (D).
Question 44.
Choose the correct answers
The value of
A. 1
B. 0
C. –1
D.
Answer:
Given:
Adding (1) and (2), we get
Hence, correct option is (B).
Exercise 7.2
Question 1.Integrate the functions.
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Answer:Let 1+x2 = t
⇒ 2x dx = dt
Now, ![](data:image/png;base64,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)
= log|t| + C
= log|1+x2| + C
= log(1+x2) + C
Question 2.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAA5CAYAAAB6UQYdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAANGSURBVHja7VpNTuswEPYBOABIeMkBWtMrRBZijWgtViBWyBLiAG53lZ56CE7B4nGC3uAtuEHvwMskcupY8V/qCNrMYiRE29jzzXzfzDgmq9WKoPkNQUCQEKTetl4/n/FL8kkI+SaEfT0odYEgWSYL9sSlmsDfC0beySX/fF6vzxAkhynJJ5RMt75sQpDUw8WUTP8iSIFMYoV8OkiTZFHczaW6OkXnwQTnjz49CoIkGFNa4I7RloLdUrbYuD5/KegbE8vb3i0APIAWL2+uz6uqUJVQuvvNQLr8MP8PulQU8i4JpBjF15GK6TN+Xpjp1gzkPsDa/IF2ZwlbvIc2EPu9n7ZD9+nIIrILcRUixAj5iuH0b9CmQzK+k8MxOnMMVEsNfDRINV/DzrtSeCnl+YLRTcN3Ot3aLQTMToLPXmHjWhNiynXTlsj55JrSD3N9GDWq53WMGDrr+1Kue/ALzDIuqlUlt9wolF34fdfz9sNlma1C3piR1sD6qmqdwW3BhVbF18vF+hUFUoN44GFdVGsctaJVf3dP35rO5NsEuI8TUszuq/XKTA1Jwz4w/eShk7uhtLSp5tuErXE1ndua16ybAFIKsK3s7dHTJYOks82khP5dF01sjdN00Rqk5PxKO5AqrHUAwtkxDEie6Nj0aTluOekCvRFZrUH0+iN1PoRgccb+xFStvCBFaJI+pJJLec65eHQB59sY6AljQvURUXMwrfYAawTkIasmhXhuUk3N5xO9oFlidVXr0p4WNcsKKOXyPJle5RpS8Bv7ZBHaAgB+8OoW6pNAP3Sm2fQA56eUbHVpdoEAz6h6HGN2qukmJ3EaRHczIe9dbYdPR7P0SS7q5DLQIrNphMYTaKPBHWrEyd5xDzWT+cYYTYehQMo+uw013esKaNOiziaqgHJDzYHZTwFSzpOS6VYKrq1HhNJ/My5eD6l0qedJWUCKOZk8FsvhRyBN6eYYzot8gu1qC7KBVFek035bkgUkNAQJQRoEpPZrlnEbZhLSDUFCkBAkBAlBQpAQBAQJQRoVSKm3REYHUp9bIqOlW8otkdGCdOhb1tEId+wtkdGClHJLZLQgpdwSGRVIfW+JjA+kHrdEsOPGjhtBOln7DzWZ/ZNjk3WOAAAAAElFTkSuQmCC)
Answer:Let log|x| = t
![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 3.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
let 1+logx =t
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= log|t| + C
= log | 1+ logx| + C
Question 4.Integrate the functions.
sin x sin (cos x)
Answer:Let cosx = t
⇒ -sinxdx = dt
⇒ ![](data:image/png;base64,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)
=-[-cost] + C
= cost + C
= cos(cosx) + C
Question 5.Integrate the functions.
sin (ax + b) cos (ax + b)
Answer:Let I = ∫sin (ax + b) cos (ax + b) dx
We know that,
sin 2A = 2sinA.cosA
Therefore,
sin (ax + b) cos (ax + b) = ![](data:image/png;base64,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)
Let 2(ax+b) = t
⇒ 2adx = dt
⇒ ![](data:image/png;base64,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)
=![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 6.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ax + b =t
⇒ adx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 7.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let (x +2) = t
⇒ dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 8.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 1 +2x2 =t
⇒ 4xdx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAABkCAYAAACB6c7ZAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAVeSURBVHja7Z2/b9QwFMfNwsRaQdG5GwjGnq9rxZRGFQsDqL3oxEDFgJAlYGBAKNetS/+BbmwwMHeAFSH1P6hE/4P+DUCfj+TSI3e5+Fd8yXfw1ksaf/y+7/n52WaHh4cMbTUaOgGw0DoJSybxbhTJZy+Pjm65en6cyF3AMmhHRy9v7YiNk61E7rl+VyrjTc7jL64GRKthEaiY8y+xTDd9vZOADfjg8yhN1wGrRhsKfiyS8WPf7w3dwoL7h15H/B2PXr/r6vtXBlaajtablqImJHglYYUyqseJeMzE8BNgrcCIJgvvs/630IKNcCTQonMnC2WM/WGMX+rCHwr2qYkgZyVg2ZJAgi4ieZBD05SzEKUwoHDd/kimDtcdACGG8eFkKzbEiU0foXxgnLxok98KJmS32THKKhi7JL+la1khhvDBwBIbOye2JUf5rF78Xfe5lEkBLE/+wXQQAJZHWCYBRojhe4vnWFfNMPQGrBUJkwELsFoA6/mDJzdvPvx1FbrfDgnWozX2c+3R+C1gwbIAKw8uShpgwbIAC7A6Akvl9Xrs+0T+xIVuzhGwPMCSkTjI0kTU4br5wc7AokpXKtJcZmS7lMFJBr5/pmNdnYClVn05O19WhkxgkeRFIvo477cmyy+dkkElQY5hVZUDFJf5AashWGRRSczTqqKYJI5f6C+RAJYxrHQ/3s5WgrNWZl1kdSadDViWLEstLDJ2MU8Ci/JIf0vbhgCrIViqVGyOBE7eW0w16dUPApYlWCbzJ8Dy6bMqJBCwAoK1SAIBKzBYPiSwU7BUMnXAvhKsKguoA6sogWRhLjuzE7AmMjWz+Leg0qjOsn4q9+8pWHxw6nqXPZb1LUWDPpoPyyIFksnWXq/X+3E1qH+rgc37Z/syvTebKgOsBmERJJWJUXDk5qx6ELji+wHLEJZuVj8rRuVieFz23RNXcj04A6wGYOU+fZEfL6nTByzPsLJotmqeqP5OJGlpgPF/Pq28ucgadAnWMlaFaNA1rPfv715BuLFcouB64ABYjmAtq0BlljOtutJLldmbsC3zAXOqY+vAqvsek+pc2zJoDRZ8lh+fBRlcxQBjQSKa+iPeT7cBK4B5Vr47k/fPnr76cD8LTMZS3kmESOdVY7UGFj2jz9lZtoyvW37mK4NBRbADzk/zfCC5GD44pZxgq2WQfr8VJ2/o99MSNT2/UBeWz7bysAjOKBo9K426sAFcEwZjl/M+3NUuEtPItXOwittvfMFSzxPDYx8+q1Ww1MEh/6pnXcPKFvI44+c2VpE7BSs/83YkDhbCsrBbf5rNtjeB79SyfnbkdzYR9CGDNFeh95rueuyUZSn5++c3fMK6ntYxqy3sBKzZI7+bgGWjELQzOx+LH9kYLMNC0NbDKgubXcLK5nAbYuckS9VQKodKu0zLq1sP69oRcqXtf2kyzWBMj1GYPJ8Gi5TjOwjdtf2HXxm0FaQAFmABFmB5aIAFWIAFWIAFWIAFWMHAclHYCViwrBbBwlHhgAVYgAWfBZ8FWIAVIqz8mILCmpYpfFx2VgbL8Aa50hNtKrbVAJYBLN0TorOLNLcSuTe1sni3qrB02ecCVknH6F59O2/jWdUamssB1GpYLiRnUguiX+SJS6UrOtfmfmWK5Eyeh+vaq0ayhZ0f+bM0r7QINWwPCpatK9ttBAYh+qugYNmSQrrhx9QiQpTA4GCZjmgbsEMM2YOElXe4hu9SFjWzQ19HWm0HOq2GlYXxdaRsYcl2DTkLNUcZNKw6UlRVW78sdAJV3KYEWDWBkYUV00hOpw0BW1TwsHJflMS7dEOPq46k57s+crwzsNAAC7DQ3La/TV82YaN8LD8AAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
Question 9.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x2 + x+ 1= t
Differentiating both sides, we get,
⇒ (2x + 1)dx = t dt
Therefore,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 10.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Now, Let ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= 2log|t| + C
= 2log|
| + C
Question 11.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x+ 4 = t
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 12.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x3 -1 = t
⇒ 3x2dx = dt
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASQAAAAvCAYAAABKSbebAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAdQSURBVHja7Z1Pbtw2FMbZfbJPgnB2PYCH421Whaza6bJNxsJsatcLw1CBpsAsikbOzmibA9SrZJcssi7Q5ALxCVLAPsHkDHFNSpyRZP0jRYrSzLf4gMBWRD7qp8f3HkmZvHjxgkAQBPVBGAQIguCQNmJwCfkK4wCBDTikXmifkdfUO3mGsYDABhySU5149NnNLPgF0EF5hT79BWzAITlxSoAOAhtwSIAOAhtwSBCgg8AGHBKgg8AGHBIE6CCwAYcE6KC1YAP7keCQOgOOL+1ieRfKSy77gw04JAiC4JAgCIJ67pDCwN+dhtHXQxy4KPS3/CDcBURgA1z03CHxQl1dse40YI9ZcPrYdjtWXxqPHRbZIPuVl+nxHWJBtAs2hsaFqb7asLtr1qzMEGNKLghhV2UzHL+Gsv2XbdpZFY3pZz+MtlyAd3Z2dMen9G2+fVmwzMvI+Eaz+4yQy/ie7HIWRfeHFD3YZiPNxTfHv41dcfEtpW/y7ZdxYYING3bHfJP3CWtXs/n8weAcEj/FnAzMosxR7DP6so0T4dAyLzxcPgi2/9rVS8Zn8y7bj6b+I1cvWt/Z2FQubNkd+tsH8lkEjLwiD/0PR/P53cE4JDF7j3bOj87O7lQNHqX+26prVB+8y6VTbvOY0Iuil8h0qJuesdg0+m5QtZWO2egLF2WTh600yJbd4tmQ8YXtKKlz6Ex+B2Y+P7rredPDXsz8uVnJRkrJHVIYnt6L4SALlTqL67pTl2xwLnw/OHBdYxNRRUG0YiuttGl3XCpg/6qUCHSYs+NFSzqd1D+u2hazV22RxY2x1zZnwqZFWJFjJ3Z3kTqoRBNx/0St4tpVGtMVGykurG86rGNjyUUqqrDFRs7uX22mhY0itRnbSzPX1ClZgI7+VxYRxA/IbBFaPFSe2xpKATM5dODv7rDRedrZVMDwuehlshVC82hpZ8TOm85YVX3sziF1x4ZNLpqyUTfmNtgQu8At2B34/oHqPbUi+S6hi0PV6pfbRiqgC/RoRD4JD1/nkJLZPQ+XDKFtvBDcIXnM+72p3fkorm8OyTQbtriQL30TNsq4sJle2bCbPxudiSxh7lKl7tQZdKIg+5B8MAWdDJdtFy/jlaFmDikdfttKKXXtFnZYjBj6wkZXXDRho4gLW+mVDbv5/dKHgOfz2QPPC39QZk5hZc4CdMUh6vLhNHgpinLz9M/SB1cJC165hC7zQhXYppI61NmdqgXV2p0uKOZn6rp27Dkku2ykD612USurY6OKC9X0yobddRyIonxmv1T5do0S5i6lM2vKXOHNdHeUmoDu+Pj78YTSf9IDy3e+ihmF+u+7nuGVHFLBdU1DaJN2n0y9vXgDIvkyYjvnJ9PtqazP6LQDNlo6pJJrdNiQ49zWbtP35DU1RsnHHHMLvopY2Ja/fSDaykVQq6LVLW9YrKpwsBK65HdVHjwTASRLogFjkcszTWoOaVWUVQmhTdnN6xJ8Y6GYyZLzVGGw/VSM+82D5//WaQdstHVI2WK9CzZs3ZPbWMDcE+lsSph7XtZWd2F5A+hW3jZ5iej4ou2qS9vZXcch6aaUbe2O+5oNq4sKqybHd6hsmIj6dBySbnqV2L0w+cxM3LOCucscc0+atNVL6OpybxW1nd11IyQdtbE7mfWu82NfVEw2Ob5O2OC71Vv23UTUpxshabNhwG6T95SRVhFzIzL6dIs52VZFkdtCnaB4JWUJXUPjbWwR6DJl05WO3VUOpmx1TaUdsOHeIWXsNnh8Q/eejZjLOZ4mbVmoE5RAp7CSwq/1GfvT5UY+U0VtpShC0+6y6EPUKAoiD9V2esfGZPKH6Lvj83xti9rKbBi2u809a5hb5HdnN23LbFhecdC0SZqwXG70/YPwNLwnrnd4YlvZIWmGvm3tLkrXODCTyeRvCU1mOdfB+G4iGyZS4zK7VbdopK83cc9lupZyLhnmbn6eY+5H0RZP2yra6h66kgcoz/Xw5UP5/2XoF4bTLcaCqGvgxG7aCXnH+8xXB8oGsWwDXOOQuaXdcrbim+zEvhS+BOuFhzJE9jzv58mEvnE5vqbZkJ/D4EvKN31/3kc22nBh0u5kpUts0DV1T7m5U5W5uraMPSDeqbrzVVW5f/w7utgOwqf58I9/sKvrPSbZpdHqFbOqIwLNcvj2dgeM/iX6SNlHufwq7+1Po0cux7ctG/HKVN/ZuO102nBh0m6+wiVTapMcFDEn+8yZK+z/jO1VtWVs9hMntWezw6rzVTYO1/ZBrg+u9npslqf4g582jQ1woTF5mbjJ6sNh1VvLTX5+pE9yfXC1z9pkNsCFI4ekoqKPmQ1d62iTC5V90AxcwCHZDWMNfsK2HxHA7Q/9Q5vNBrgYiEOSM8e6hOYm/oIKlI2S1oENcDEgh7ROM2Hbv6ACrScb4GJADolL/DFAhW/09lF8fwdWUMAGuFgDhxQ/uGH/Ke30/goIbICLgTskCIIgOCQIguCQIAiC4JAgCIJDgiAIUtH/oL+MUMLiqL0AAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 13.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 2 +3x3 = 1
⇒ 9x2 dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAA8CAYAAABsKjQEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASPSURBVHja7Zw9T9tAGMevc2FjAXGZCkO35JIVMSDnRGGkwnEzARmi9KQWJA9Re7Bl4QswwdhKXRkKYxf4BB3K2Il8htCcnUsTxzZ+PQf7GR4pg+Wc7+d7Xv73nNHZ2RkCe1kGkwDQIg4CoVdeNi9jAWgTxnlzmSD0MJyYwazhR8p4OUkQftd1NHzsPg40wFrnGKBNQKugyk2T8+U07t/rtRYoRjf25JOHpmmuhL3HqUF2AJpCaEwjh3K1Ngi6Qqv0ttXrLQC0OYY29V+MljGq3If9L4CWJbSI/1UoaEGCf1LQgmSgYqURjR1CTPPKxHTtXZ2ULqzg7wMkCWjTyYbDiHEprzMoPQgbzwoDTaTOpRL6PZy0p7SgCVAa0b4EhSDGRIzTnSjPUyj3aGVrKUETEIJMpHCPw2tPhteeiN+m2VzRNPYeoCmEZpqtxQZdPR0W3v2tdrfy3PUGQZdxC3aAFgMa1+kGRujRdrvqlAqAFnOlSdlL5SQCtJjQxAQK15iEJgnQFEGLKkUBtKxiWgauEaDFhJaFawRoMaFl4RoLBU3UU7SKfghoop7y0iCDQpt0jWISo6obAM3XjXlrgJGgMX1tCO0PxtVrarDtPK60oC0Omb81nG++XUJLfzc5fzsvb7LTPrxB31+Tj+dpeiVm1PYxxr/GLzkmd3vt7nq3vVVx7kzMATR1+2lxYnMQdxylAaij13SMUF9A0hkrOz2LUH+c/w3QEoIW5TlGjURPmDTO3ZIrO8zMJnIALSNoXCe7loZKGle+yVepfuEE6hkEVfX/FRHa/7ZB/5rTuo4YXz0TkdktDDX9f0WENsqufVdZZsV1nqE5PZDYXLWewzRXnvNOtugwm2AohxbUvTofIii0MPcPa1GgeXimp+fqU6ufZRXdxpHjEotpQVyrtIjQBmmZSveYKDSIaepi2tg96nwXYtrLSkQGlvhtmovush0tU51vALQ5qtMYxZ9tuapyL+QqGX54q7VsEML9mmoBWoLQCCI/wzwHM+h2FePrqfCDq9c642vgHhVpj6osvRsHzDpVQIur6hQCWre9t17B6F4u+RKpX3gG3JS3ZsYqulVD4b4lznqMxcvS3prJHJrY/xGTVDPYvp0F6WvW4QiPNoE0obluxgp4IVsWcg1tXDg6NDW/Lqq0oNknafA3+fLIwC87lMO4u1xDs09aor4bHK8mn7SgedU5UqwFaAGg2Rt+s9KN6nYDexz+HWLFgib3iVwqfXuluUFTm/KLcYSV4nLfjSU1TJmliRSbMb1sZ5Nu7jE4tLiitu0JyB2cuXar9DVyOAr4VlcRNejBeAU6srYw0OKI2jIxiaKsF/LrBrKBxS34q3KP4kWC47sBTezoWqsM0xv3Oi19aG5HfcMoI4WCNlZGsHccSRtaRyNHROscTbcGtBbrJXIR5kxcrqGNtxdo7ZMV1zxWmApo4oD8qAVg1kI01eQa2uT3PIL23KcFze+LcsLCxDf4zFJGiUgcA2gADaABNIAG0ABa3qG5tFPPy4enxQkXgOaANjo8l9qHp5MoEwAaGEADaGBzb/8A1OYLbg2zyhgAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJsAAABACAYAAAANmAVgAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAXwSURBVHja7Zy7bttIFIZn+7i3A426pLdGbrcKaCLOlg5CEarWUSEIA+w6gAoDod0Zi/gFXMVlim2zwDplUlhPsAvET2A9Q7QakkPJFIec4UUrin9xGuo++uZc/nOG5OLigsBg6zAsAgywwQAbDAbYKl8oQn4ShrUAbJXayLGODln7mhB23/e8PawJYKsGNIuettvkn7lXmwE2wLYW6zFyA9gAG2ADbIANBtgAG2Bbw48N5YssA2yArbC5jHycw/Qjy6g1OgVsgA1hFLABNhhgA2yArV42Hg927C75U8D2YnjWQY8UsFVi5y57tVJEMPcj1kZd5QM2WCUen7sHbyilX6ONSNnd8fDs+dnwRYdZ/ASwwVY8k+lrRs6BQwl5EHA5nO/L6x53njFCvovBBeaevwJssMg8r7/XIZ1bk8JHTML4eiTrXQ0uL58kpx6rxRQWHLAZwRbmsDPCejdp78nah9dxEJVJnkkrB9YM2HyICLknhE5t7u2nPo+575UFQpFWDqwZsOl4NUgfMGUEG4/7T33YxuOnWVEsELZXE/+1w6YbhmHrs6T/SRHBZlla4uXl4IndIl+yQqgWbEVzNp0QDFuvlRlGS4UNOVv9w2LVOVsURh3vF+RsDTPf21ByGzgCdi/yrjUUCD9Iy/4yGI93Et+P2/u24/0M2LbMuMVOZEjzI5OAIEFkLVNn4zb9PWhLdSaiLSW9qjcY7LmMefEWFWDbRglj7lEo6UxMR6AC7Yz9bfI67tovu5R+fpRe0e5nh3vPEEahl21Gflm70DHfVVk7aNs8lu3ylzrPSwthgM3QRIKaV1CsQ0WZlptl/W7Xtn81zdcAW1pOwnpX2waanKAQ+pWYAlZXnfSTSt8S71GHTVibP6XH6FVeMXGTN5AMfT50KT1HX3aIPS68oXgdtUbvZOvJsvhrwFbUq1H706aHiaIpQppgHhQAdLLs/VaFePqwyRuyJl6N3Gxz50KMV1uWc6KzDnknLrYWNp32iW7PVc5QZeUk6567K+uzAn2MPOi0AlUTsI2FTecujWfD4+cdSiaLQxKdiSo5DhY4vfkbzsNPg+kFOvXHlRXtlNJyLUruZGLPrNHbUgqFjA5ACOa0rhV56ZVV1l0a5YJR2/XkwooTOiqggmpNDW7iUTvx+QatGxPvJL7/ge3+Jt5bVImuTd8XmfF65METRqmTvHxdU4rKciwVIEk7WI6vxBdxMdaS/F5SEjhw+Rt5TYi+YVjSAsBEeRef17f6rxO/Y97p1TAUZxUIy7DVNW/7f2CLaUryD4vDES2uwkupJgzk+HLZsKkATNooqtx1+VrU1NY8+ByBnaPh3kjYFgkxnVrO6CjSipj7QbmTDRc3K/SWCZs4jJskNg+Hx50upX8teyHRCQjOWtq3eWDJ8vSALb0Cm7VarW+q3p/M70zDholUkhc2IVcEhQn9V2wadR4ZeHExflO0p1vGtGzjYFsUBUvJfEL1mAe24DXsTvXZRQ58xDzu96X5/VkS3P6tCcT3n1fbZcAB2HLAFoTN3pVfzTH6Qcof8UlTU9iyeojC8h74SKyEOd8Nv39i9V12jgXYDGFL0s3CZvTKecQINs0/S2c6ouycbfF780k3gK1C2FSP+ddjUJkUCGFD+tRUPysDNpXwLN7b7nb/KEuIRYGQF7ZYyEzT37JgG1nsrVDxH+dig53DNrvO+lNMYUvK53zYlipM+biYMePnfLeIDgfpI6NKS7tLY1SJhkWBL3041pG4Ft/9Ojt5Duk7maSvmMYfbHSvizCst9nhtTzs4YvIlH6VXk2OConr8pr02pw7+4y5Xt61hairLPnVifbj3mJwA7m0wcB0gVh9xlVX1NU98PH46Fww0iP0Qc7Pd6O80Rdq6cNyV8PvDsw3k3huEY+EdlXFptOIb4qhEV/1AmuOGDXBMGK0Bqv70CDWoUawNWEsXC9fTBesAVuJu7rJoXQbTpfVa7Eb7N224XRZ7RLkTT/1XYWJhv42ePUaLnzzbr+wrNkBNhgMsMEAGwywwWBV2n+HeWvcjQTE+wAAAABJRU5ErkJggg==)
Question 14.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let log x = t
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALEAAAA7CAYAAAA0Amt7AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAbSSURBVHja7Vy9btRKFJ7bQ5+VMttBnx2nhAo5Iy63jIRjpQpssYqMIFdKEV056SICD0Aq6C4FbShISUOegCvBE2SfAa7P2OP1OmN7vGt7PNlTHMna3/Gcz2e+c+Y7Q05OTggams2Gk4CGIEZDQxCjoWUBScgf0hDENScNAWTejn32JPLFr8h+E7bzAUGsYfue++cWG54Twn7uhuEAgWTewoBvUEKmzD9+giCuArBLD4ZD8l089QjinkXjeX+cno7vuMz9Z3x6egdBrLAdRj4giHvmj3V+mQUsBBzq7h9gJEYQ9z6RC8PdASPkpwTs4eH4rs9pSAidPpocjYpyFwQxgtgYeCEnYZR8g2RuyLbO971NDwDLg3Aj9PjDiBtfx3RPJHu/iqIxghhB3LlBhN1h9G0E2GvuB4/htcDffAoJXZZK5CMz0gkEcc/mPAJwFHHTqoQCsHGSF0fmzkFsU+0VQdyt75Na8O98CS0urdH/soBVJXmdgBgGM6LkCoDhBeE9BPHqWJXvoVTG18mlCph5wOpSiVZAHIMCiPj8coEgXhWaUOz7oo0MiM6CD2d26XSpROMgFk/PcOu8KvwjiG9hFNbwvYpKALAdx3mXB7culVh5EEOWzB3yCUBcVoe0iYuaugcd3yeR+DqiCH/DOAOfP2Zu8Aw2M8AHruu+EOW1DJUA4FdtQTfOiSgZXdkQ1TJik5kx/72NAF5UOGPC9z6jb8RYKfuWltc4fSUoiBc+jH/LuxeB+AelzoX8TMcgns8w0boEUT3hzG3xPYL4lphKOIMgRhDbVxnQTIQQxD1e0lbJyoQzqgSv7aTPpO+Vk1JmCGLz4C0Tzkwm2yOH0s/ZBC9w2TMhpqH8iypS2+77TNZI3t/I1hVWtoOCIG7XqoQzcD3zVSxf9BkLq3ZObfc90gnbeK+GcCYFNh1ddcVRVwbEussW2s2lu45wpkyjYArEbc5NC7yoOEPVWbLQYsvOWx3hjDS5C6ZTcrPN9x1wYiyxdRXlVMIZSTG447zWXd5t932zkx1N3ojQKwRxs6YjnMlGS5/zveA4WBPRu6NtaJO+RxBbFInLhDOOQ/8FwMJ7cv4l1QgCb4MxP0QQa/Aq4G5bQ3aOssZq/imvs6+XL/nlwpkY0PR60w+e5ujGNWX+mzYTvKZ8v+jcNPYUQpmH+f7zskMuVj6ixvP0QyRcwe4D2LAAnileT64tvaelfb/M3DRyIyJ7puSLLd0cpqkB7LLt7gYPxOaEwz9x7u+Ja0Myyr74ftG5sQ4EYtKiG+tjtIexQVI1Pjy8W/QZcZoN23kL4wfOOndtYSRu0hadG6tuErZdS8/kMtzdkC6LjJ+pgBxHLfpRdi/IRGgVE+L8+WrLzI1VNw66gbKbmdU79RoMW60mRFFE+TrlH8FxomyWLJHiOlo6VymXyJ+vtszcWHPTItNWAEP1uT40fsISmN9ogGqCdBw8cPJ9uB46/J0NRxw0sZpmz1drYm7s4cHr5FJn90nURnuQIImHyaBIvZdJbY3z1eqYNRm9zpbmrNxjXkWHW/DlPmoyiTV6Q7odCLpiliIqoStkqfpMnY6JNpx1G6zOoSi9B7FuB0IdWaGKSoTj8SAWkidCFjq62p4c3b/J0zZfJkudOMGGufvPs6Cu2zFhQg5pR3LefC+gwadRrwNBRrQqnquiEqHH/hKag2TbVQWs9LVMt4TUKkjuRin9ukjHBJ4u1M3qZPSmdDoQUkBVgDhPJY4mj0bx9+YPRMkvZzFVmVeIFUXRuh0TSSfGFHlxe1TCOIh1llxdEGepxCy63oyCiVBmOqf0yk1s+gDkxlWXIuT/C6lEO8cKGL+xqqQtI0M80F2myr6TX+IltZEc+GiyfV/SC1WVo07HhCrKI5XQO1/NGhCLDgTGzso6EHQicX6ZKupHm1GM+d9KErRpWrukzkURP68aL0biopJjvfPVeg/iOh0IOiBOxd/wW9zfU3EvcQKmTOByoIJzG0A0XqbJ0B0vcmIDeDJCH2p0IFRVJ7LLVOh5G7DMp9rU6DsgxInPa7jZ7j5HPUAxNQ4H+bpv3fFidWJVQFyjA6EqmZLLFNRqsxQAwClPyYH/g98OguM11fcdSi/mGiKp83l7MhktMt5Fk0A0ixO7JpK/RQ24MPSqpeAMgjWgDAn4l0rIJIhxxw5BnFnym9UhlKnd6giOuhwzmsUgbiOqydKa4MIRb05PmByPByAVhCx6mciPKjYEcSeggGQtz4fJcPh9k/svl/0flZ4YbcVBDAZt6zYAo6izAw1BHNMKxs76XLISY3Sc11hWQxCXg6Tv3c7IgxHEaGgIYjQEMRqaTfY/IN4+mwwbqVoAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 15.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 9 – 4x2 = t
⇒ -8xdx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 16.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 2x +3 =t
⇒ 2dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAxCAYAAAA2neyeAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAP2SURBVHja7Zu/T9tAFMevO9kL4rzBji9ZOyHn2sJIhbGYAA9RdFILkoeoGLYM7R/QTLCVoStDYewCfwED/AXwN5D6nXPGcewkTkw4K294UkTIxfc+d9/34y7k9PSUoOlr6AQEhIaAENCEgxPyDgwdrSGgpm19rjOjQwh72PX9RXS2RoCaFj00DHIX7J4uAtJY4nYYOUdACAgBISAEhIaAENBMAKnaqqj6SvdarVSA2m13gVNyFTj0WY7reUvTlgPhWPSJC38NAU1pwmL7ypFy7GV+7bbbC5OM5Qu+xiyxH4FiO+cIqEADB1Ni3qqxk1IVfw07z2LW9yyYJw7boFbzcK4AeZ5b4VXyBwCtN1pm0Trv+7uLJjGvFCCHkTMlVXJHUH6lgAwDBM9pWfb+zB0fi6XDfPMqXw4rMtT2mDHnrOgdpCQqHlMMVu9w2/8Qd4KEwKxj1/MqcYeEu5A8wvPNagfBswintk0p/Rf5hrKbrUZrtdVYN5NzKm366XC+l9wR0uGUX8Df+xOK4YtF7ric8WwSRWjaNTtYEE8AxBZi7eW57RVGyD30LplzslF6QODQ5ETS4tK4MQjkkhn1zriAkvKaI2PsUrbzM+17QtUZjNf6Fmgp+gyvg4keBXJ0FErX7pJliS9RzOPOHiQmNUdsC3HyfhQgNX7eJCEvIN9mm7KzPyRTzFokmUEry2ah0Q6vfVWxIV6jhIlAXK7oI7wnV18gG+AwWKmUOT/iE00D9FID5Y+PeQBJxxPyMKrWkv/HnOPMJGFw8un2msG01dhaNSm5Nar8ly38FRlHlsm1bjVKHkC9hKk76Ry0mTTIlVxpsdX8AqjYDHDalBieVQLyvKVRChPWgoPBv3SAkkVtL94EMsTu37rZmqEu3VHZYbTApmglFRaDxv182jiRTgcy4LvuItQJ8shcpqP+im4JzLgSVyigaWPQOJ+NW6pOw3uGcRfGIKFl8zJvDIokzvY3SytxCtBAkRbstLSCtIRJwrMshD2vktUVUd0PLQH1JO4eJgEtDwAD1fVHSn/r2MTMWwcJTr+FLR3zVs1PzjGQc4cxP9ne0TJJkL01Sm5UfaNSbV0ljhH2N0/yIhz+qUrpZV+4oNXLUXMsbS9uXgydMK+AZt0iQkA5LGqry9SZPskObkYGgzZjQKmHdQBqivsDCKggCw/J6AW0++PZS68zPXE/CgEVmCqnFVxZhSiaJllcr+mJN0x1BQT9KF2vNc09oPCeQHjaiQ7XDJBKGnS9Vjv3gOCqLiYGmgKSlzcScQc7Crp0Eix2wKzmQf85vlupG6yDseiNAcG9td7p6KBp+guCuQHUd9csxTAeaVoHoSEgBIT2NvYfld0lIVWON8UAAAAASUVORK5CYII=)
Question 17.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x2 = t
⇒ 2xdx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 18.Integrate the functions.
![](data:image/png;base64,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)
Answer:let tan-1 x = t
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= et + C
= ![](data:image/png;base64,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)
Question 19.Integrate the functions.
![](data:image/png;base64,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)
Answer:We have,
![](data:image/png;base64,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)
Dividing numerator and denominator by ex, we get,
![](data:image/png;base64,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)
Let ex + e-x = t
Differentiating both sides, we get,
(ex - e-x )dx = dt
Now the integral becomes,
![](data:image/png;base64,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)
= log |t| +C
= log|ex + e-x| + C
Question 20.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAAAdCAYAAADYZew2AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAUdSURBVHja7Vs9T9wwGHb3di8Vvq3snHMrEwouLSNVQ8REe8MJpSog3YDawIYq2r2d2o3+ATrQPwC/oEjwC+A3QPPa8Z3PF5+T3CUxqodXCveVx/bj533eNwYdHh4iFy4eUrhJcOFI68KFI20WaIQeiXD4HWkfRGwQ9DNZ8DuE8M1yb7/t8DvSWh0HIXlFwoNXcL3t4100T/90j44eO/yOtLWnyzLfi+PNuTZqn23G8ZycdtVrW0PFn2cM047JZmuSF1vlNzcB6Pe7TzYI/iLUp+iiExLG4u+QoB+QdkkQrzEVw/SsKRVT5yBrLlL8n+TXJo0hjugijLfb7z8pq/LclqB7RDZ+2paB8mKb+c23g06AEbplN0f4Frc3vuomeb+3vuBhfNoJozdl7hX5/mtZpQaDx+2LIIqfN7UAR0fdxxSjs3QRhqFsoiz8pjFEFO9g7J2u9/YXSql7QnxYnzIiUXnm0WAbyzYV7RY57rN8W7+/+YwgdF128uBemEY7eVKurd42C3+eMfB5Jteb/f6zcmuUfNfC+cnCBgLgE/+jzJ+ZqssLjE9k1YxCuprsnBsgrkpOVkGT8EeZtBsHZA1SCFzv95bbNIiXhNUIKd2i8+iPjUpiwj82hsQi6H6H2YgSKZ7Nu6XFn4oN5gcsEva3dytRWpB2efIV9R0hLSwURviSRvFiUW8M6XFUyckV7EyeUsk5XPMU+uKkLjUp4uF1+Ie2IN8YeCrFl6aWmYyLeegkuwkS6Aq9uoq0SdhYrUPnD8BiwhhlTMbCwVRMGD0uFBPSwuTd7VxxOh9Spb4T4G1Th6ZwMt+cqLFObZlKBf5LgtE54GqRle9QbwA+EIteb72d1BO/xffh85FP3rJxZBSws+SHCVsc0CWRocXmltV2rGo1hc6HTZJ8+YamyRYFWiLFFy2PfoNiJM93moimceo2v+jIwMMLGkar3Kp13rACOfk8XA/XlG+ykJB4UvGamx9KKtd1i3TYBp0SRXkrb3mN2gCe7kbaPBowcoEm+10YKCdDcQ9ctCWVVzmycA5JOzuc5izG1WmMzEAK6fWseR+QBbcvTFZtphstBzZuK8fHVilpedsH/1JvKtoaOtLyQQ0rSGHGVYsxbUybWerCWZS0rMjLKHyz6ojBJqupMBPdJRWb8OcytkkWsjLPAv4oq4KfRFqx4yC9xt3uHChBq4X+QnHSZN/VVpwqaQckzPCkOhKkG83YApuWH0WwmbJxJZ6WtSmUz4nByAuu6zSwe7Vaf7lXjBZtIattOFXS6przrCcMNkCZc1gL6nmf8zxsmNbTFsE2yRrM3B7wFEneEX/7nbzzwJOutMh32M2TipVBe0zpT8JvQO/Slt6iLThVi5LVXgSyeJ73TRBGVkPAGh1ET+X1qKrdlQdb3u7SjAmL91IFGg+JpLrTTakKX8F78JiSN9/XF+ChRdGuRQ32oFGcWUVfqmY3idrtMYsW0tUOjbaEBfB9/73n4RNYC3hPKJkgCbTB1LMQs+zjm7CxdpdkDeQTcZWQdrxpPhrqDtM1xtmhkLR/B1WmaCfZZhGaxplVvPA0jo/5OQdyPmgpsbVJKvYgXhLX8pPLNEXfYBIeV5klTNj4uILnIAhwvkJ8ptaWl9EjWdZ3fUjBFKqm1ppt0XiKhR3v/u2kjD+sr7XmSKsQF44mYhrG7vR+ThsGDwSS1GmjZfovSCsKCvA6tp7Kss5HJ4XS/77BHRlcONK6cOFI68KFI62Lhx7/AFQMErHuL8DtAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
=
log |t| +C
=
log|
| + C
Question 21.Integrate the functions.
tan2 (2x – 3)
Answer:tan2 (2x – 3) = sec2 (2x – 3) – 1
Let 2x -3 = t
⇒ 2dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ 1/2 tan t - t + C
⇒ 1/2 tan (2x - 3) - (2x - 3) + C
Question 22.Integrate the functions.
sec2 (7 – 4x)
Answer:Let 7 – 4x = t
⇒ -4dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 23.Integrate the functions.
![](data:image/png;base64,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)
Answer:let sin-1 x =t
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 24.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
let 3cosx + 2sinx = t
(-3sinx + 2cosx)dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAxCAYAAACWAoRwAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOVSURBVGje7Zm9TttQFMdPmIGdiuuNB8A3GdmQuSF0RNSxPLV4QJErAlIGWtlsGSp26EI7dWLr0tK98AJV1fICwCtA6mPHwXHiXDfcJNeJkY4UAb72+fmc//kIHB8fQ26DLYeQQ8ohZR+S91No21wWzh07JHSipmuVDap8BKA3puMsyXzuRCDZjNQVBX55r/tRpDOjOneimlSl8GkUzozq3BxSDimHlEPqU8HmeOV9piEd7a2rKoFrvEa3nZUcUuL/wwMAuWW2s5pDipnjmEtU2Tizms35XJMkgRSONoG1ChMZSyxre5FRuEBn1veOKO9BHJutElCvBzk+zLlJ5pq0EqQ2tIAa52OHFHmAJ6P6OR8S+T1Ii4Y5l39PuKeGuxV9EdKuStJAEn5Pnb6Mpm2jYS1oVHsfT/mZhlRV4TMQ9h2h+BsGjRwSZtclj6Tu0Betk09CDYVGw3zhCdoN0WoHqHNVtux6rcd9oHPdKdf50Oo+ZJAVsgYp3ENRAleoY0qRndb0ko5QGGO2d99bX8D9FQw8xKOp80GncN4jin2sXzjKDAl1pqqSE79BNfbL/l7KKO3gvcJU89sPjKoE36Y63TCCXqHuALmLal0cSiDgXlQl6OFUQwqch0dqupX4jBgtElEBHwjpuZqU8tq5pCmfV93+97xm05pny3AZdx6f34eyzC7TpJpQTUpzbdSGgDTEeb2RidHl61G7y+almlzp5r1RFci1qD7JNegWVqwQEkYQgisWi6chvE5UYbQ1GguJWTKtkNqRdOf1QYeYjrbBNkvMfu01jAfYZWua9pbZxma7VzpEqHHtkgoSOoGlekOhZyLXHwYlH/x0JPRnp/wzUvfbAdNdc2x9xYP0R1GKX8O/SwkpFE5qGLuMsndpViVjf4mTfgCsQmUC33jbyKmDBL3tREFG5ycGKZiTSrpfZv15iNwTtXqybVmLo3ohmYMUdrmxPqblNW8/sMyKnsv67X+khhToC/lSMuyd8Hf7BitjKY72LMIiNmH/IzUk7E2wtPIau+fC4e1/Mlnd2g3cXxE9kGuyNd7+J5OQ8CsgkY6kGUozBSlYS9ArkZ10mqE0M5Cw+qCQi3aGt//JDCQUU1ujb5KGxqyk2kg7bhTrnoW6gCo07lQbXcet0V2q1XajowmWbRFTfpr9j9SQwgavXZ57jfOde+pU4+x/pIYU7GqSV6zPdSrt/mfqViUzuQXIIc2o/QMZxRcWV66LZQAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 25.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let (1 – tanx) = t
⇒ -sec2xdx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 26.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= 2sint + C
= 2sin
+ C
Question 27.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let sin2x = t
⇒ 2cos2xdx = dt
.
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 28.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 1 + sinx = t
⇒ cosx dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 29.Integrate the functions.
cot x log sin x
Answer:Let Log sinx = t
⇒ ![](data:image/png;base64,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)
⇒ cotx dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 30.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 1+ cosx = t
⇒ -sinx dx = dt
⇒ ![](data:image/png;base64,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)
= - log|t| + C
= -log|1 + cosx| + C
Question 31.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 1 + cosx = t
⇒ -sinx dx = dt
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL8AAAA7CAYAAAAqy1vIAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAkFSURBVHja7V29cttGED4qre3aPzp2dh3xqNKpPNDJfx1tQxg2dszJcDRIYinDwrFJdxpHTm07hX+azKhIl5nE1gPYygM4GckvIOkRJDm3dzjwCAEgSJEACG6xIw0FkcDdd7vf7u19JE+ePCFoaNNoOAhoCH40NAQ/GtqkgpmQkrAZZRszCH60qbFOnV0TwD8U9oUw5zWCP9xDJPIMaJNnbZfPUUL2mdO5HowKUw/+drt+jhGyTdjSKwRLAefXZjcIYTv1dvucfq3Vapy2mPWosbZ2CmkPWmFtiZE3hPL3Gujg8ZsWXaXcfTAVnr+b9KhQZ/ycCf5tI+S1sPcIo0vdBAspVPYJLplpternRVT/TK3lFfhbo1E7s8RnO4TQ/SvNh+JPX0qFBv/D5pVKhZa2IPGhzFlvNmsVbre/8ekOIUeQEGlOKDzFK50kgXeAQYP3YJR8gEFjdvuG9B7NGmOU/kUqS2/1wLt8/p7gl7uELrwLhlS08QN/2bauiXn6KH4/KLOFl8s2WxJztsfd9lynzi/LuYHkV835IeXNB4UF/9pa4xSfJZuCz78BMELywwj9CIOhr1kWITDICQHslND/5KA57Po8d35w2/ZF8CLwXkYV4dDzIhWHsce2276IQEzfgMPfqdBfxVzscse9Cq+5zvxtSHRNyuM5PBkJCl/t8R52RzzsqqYrAFINdD0YwTKYXBCzfNN1r1zmzo+L3QVB9k2u2B3gypa5oNDS9fh3KuStBL4xB2FAV8mvigSpgV9zsCwGx+UUqMvRnP3oZngloEt5zGgBYZNzt9YbIei+OXDyWkrew0JBmpMNBtQclo6CpUxwVmVS/tecr2DyO3bwK85N/hHU4nNWtMBhdL3k0ZOeSoD0GGGUpzdc+vQpZODEoliBZzPfAy0UA1ujxkDUvEA0kEA3nFI/yjMW8MubUNx4N01qYFZlwjx0LOUBT1LvXAsuiGB5DKoJvFp9KjdRRCKMQE8XA1EbWBANpAMz5rYf5Rk5+CXAygsvs6AEyxa7X2+1zgce3qctZrjUC6WbIIctCPW/qpy2IUueDuf33I57VifVXqmthIBPBwNQjJC01XM8MPawIKrV6nPtkPR8+JSn1TodNUeFAL/29JQ7j2uNxhmo79rS+7BtTU90WGw+rF1izHkc5Un8BSGuFWC/u7hI16G86Tr8ql5IDiOvyezCJpRR9XvlJRkcpLFr4sC/wr8W87VHre9+gmeEOZnn7j1NRS3L+h7myKA8q7BgzKg+PvBLMFW20ubD8LCQrMrSpqzPi5BL2QfNNwHQqp5Pd6GMqSdGlTC7C8SgR9v6/1UCLf7PcW/7kyD+D2rIlNnreUp8B23sGstcjBkDS4z+AnV9mB9dmWt6cwT7OeoeZJl6u1yu/qmvSQn8ql6OFCAj2hHBi9P9/MnAAIK/aOBXjV2ZVaMQ/Aj+7CotUM6NqW0j+McK/uxC7rRZZGOX16OURSPeJGHA/yXQ3RhnJQR/PoDfvG1d9xu7qvzFsj1v69q22YinS7L9GvGmDQNGFu13N8ZaWF80gj9d623sUtUMs7ELfpcVkW4jHkvSiOdh4KA/BpqFwADSngn0+LGNXccb8fbSbMSLw8AoIsvEgp8kf3i0iMYwf6c6sHFjtmXr17JoxIvDwLCRZVzjOQa+F53pJ6FVaL1mjl9sYxdEgxCQ+414RutHlKWBgSGj3cE4xnMMnB9LnYPYRoyXT+pVwxq7VG7gN+LtJWnEGx3nzwYDg4zl6GmP4J0VQvGgxwCJq6QlAnAlwnZqrdaFuOv9xi4P/EZj1wu9KHQp02vEu5t2I15WGICxXKTkXdKxRPBnbFB67G2Wi+fm3cau5mpUY1e1Sn/PshFPJd69R0fzOJYjBb/aZGmcXiizl3jQY9hEsX9DmM3oemRjV71zOctGvLxgIOlYjnC1k8/Mce5zxn/GI37DjiF7N6mOQ5+fzgMGko7lSD4MqhALkm8Nd3Kn6AdCkjwfeCugMJP6jCfFwKg9f5KxzAUwXMu6VVQZEODpzHK/DQomBccATolhxDy5YxlkLDO/cYexdtETZMm52dKzsAUgxZdEwqo3rfBY5GAVHlODc9CxzPTml6M0FI1uxaJMFCSipp4QGNSlpY6kev2rVqt2wbLcWwjsZI7T1ODsjmUz8VhmdvNqO/54Rq5l6BZY+bciSYToMrApp3J8Uyl7vjwJoA/T4BxmLDN7CLkdH3LOFDxkuUw+laS+4mDgz3ukkPVnT+sTbVgK2V+DMzFesvP68d2fSvslOfiVZ628z3OkUDu0yfps0OLnup8gVW7Br3Yke6UAswJ/8DTUCa4JlUXvuUfdm4OCVycDfwJBqtyCPwmw0wC/5I6MPvPC6GGJihzE8MoA4FajcR6u0VwSrqk1H14KRrKALDrTMhphHgv6bBDEJ8TPCM4pp37jpihU3M2PG/wCsIyS0l65yp/rPQbIQ8zq0yN77iZcA4CGew3rj08iiz7os6ONn/JkAn7f+50Q/MHecyhtCfBvQjdfb+/58cPaKuco9Wo7CtCWSfmTBq0vYBtIyhVvN2QQfVn0Zqgseij4Ueg2c8qTDfg93tsv9PcDf8T5g6Njr4V88Vw/eQ8DpDvBzw/LV6CxrOTJosdtrHTfNz7fQUtAeWI0OAsP/mFpj/78uLAZd02YzLny9lIWfS8oi47gHwvlidXgzD/4M+L8wQMhwapO3DVBKtRPFh3BP2rsJNPgLDznPzH4jXKj+hK62iU9oJrXm15c9qkr4Po7h/1k0ZHz59tyV+3R29eckT8AJGr7ur/C2IC0Zw9ONoGcuT4RVa3yp4EvstgmzH6jJc/VYuwCP4ksOlZ7EPzHTG7zR3i/3m8+jE5awyMK+zuJR/X0bHZ1D0hY73eP3Lm4Bsqdrts5a35eQBb9wJRFj416GcmHo+UA/MFy4fRwVhT1mnrw+0fepmyb35MP30G+P8Xg96nPlG3zy7wBKQ+CX1EA9nFaOhyVfHj6kh5oOQS/TDzV6aaVaTi6BzvDcWp3aFMGfkV/6HrRE0BZEcrRtzai5QT8KgLwWpHVGyZZkgTBj4aG4EdDQ/CjoU28/Q+2x4LPVJTwlAAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 32.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAAAxCAYAAAAlSqxqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASNSURBVHja7Zu/b9NAFMdfOlNmKD1vsNfPGdkq56CFLSqOlYUKD1FkRKnkIUDSrUKFmR8DlAWJgQ0JaEcGKH8AQsA/0PZfoOB37jVn44Q6KXGCb3hSlFyS+n1y733f91xYW1sDHfmFToIGoAHo0AB6/HEApTCmKDSAHJLfdOyFChpPAfBHvd0+qwGMMHzOVgwDvoRb4EADyDFqCJsagAagAWgAGsBoAYyL/CskgFZj3jQZfKYLd/z2eQ1gxACii4afAGyX++05DWCEANrt+lk0Kk+89fVTugdoABMDQLVNAF5NDQ7A53MMzJ28L5guyPOqpznCawIw32hhlgsbdXTquBCVbfgF6D4fEgD7mnftVy6oG1h7Ns67IMod7KPbWZx4AJMYbQevZC2XGsBJ9isTXgDjW1n654lsoyJGvOnCVBDUZ8Im9YNxf6U7yHZ7Vnd9vI9pAAMmv7FkLyKDT9SbDIs/bjplJ5yb9qlyNBpVRMbegll7cZj4ks/Ly2Fed4FV3qs7RAPIGEHgTddM9lAMqe6tS/Sc75aXKGdUfuhxVziwfVJvLuK9Xo6CBpDxl3+N6nzCIRCzk1J+FCh7wMydfv1UA8isckoHWO8sqM+Td5YULuvr3inOYAtm+Xa/ppxJBalNpwihXrtI6CxsJ1UO7QqhflIS3bTZbSFLg2DmpAD8LFIcpzLQrhD1PzH9kirilnWfyhA67SuZvCAT2I6eAxKTuYuLZDNIAPTLJyiWZT2WYKTMpNdczq/7Hf+M2DVY25RqSAMYzmbYY3ZzlRLtu/xymfvLsszYtn3TsthLkp70msyfi/AcZivboTQ1Ed17fQFEA4U3XTHwyf9q/w4TLrINUZ4YfjySoJytCFVU71yUj8uuv6R6WqT/GTobac0YklIKXfcGR35nXOzo/17aql2+wuD9OJyCFRLAMF6ITuSIAUz6fZtpamSiAAx63+Y47BYSGTbad8elxw315izntZG8Nbfy3C1i59psVfVsNICM/abXLuq3Rp4v1/hsRzqUaQfovTz7QgMQiUP2QHjpoQYvMXNH9VYoaYHnzdAaaSHQmmqjdaGrxfnFw/f/AlE26XyZv5aevfycXp59YQG0GvPIoLRnWPyR9NPJ+FJLyF1n7iqtYeiKQaeXC6laxvEDf7EjzH6e/UQCeJVwFoOgei4EsF0NgnNx1zF9u0cWbylmcpEdYIDxRc4p0Zo/jbDIt4lOp1TTLPlc9yDFzM16+WcAwteepTiMB8e91eRvB9xH9jDg9+T3R/5MPNlpn3dcz75wJUhav8xu3h5kjUi2AibtxCoOK79ZZiwBJK3ftCGq15q0spRWfqKZ4Miz3+/n2RcXgJIUSnyrUb0gXUhZ56mBqkNWRZSluJ91VH6CYDrh2S+rnn0eU/LAA03W+zYHKEF75KNXPe+09N8ti9+XtfqwrHwDdDZpTSRX6QfR48Dcbq4SNMbYh6ye/dgBGOS+zSgR+O64tfZQoezK/1Ogw480UKFO/SjXkBT1/c6Z+BrnPIEyDOsN7Z7+nr27MepmrB3JSbYidGgAEx+/AcXEV9+VHi0WAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let sinx + cosx = t
⇒ (cosx-sinx)dx = dt
Therefore, I = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 33.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I =
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAAxCAYAAAAIlEGVAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAXsSURBVHja7Vs/b9tGFH+U1/xZE8OnLeka8+QxnQz53DjZBIcitDSoUAgGkdotNLiO5M2p086NOyTOUsCfoEjsPUn3Ak2iD5BYHyGxeo/Ho8+MTFGpZNLUM/ADTOpIHfV+fP8fbG5uAoGQFPQjEIgwBCIMgQhDIMIQiDAEAhGGQISJwx5AAQCmAhS+ZI38syBcs1cIjq2Tn+2F1/XUuSnzHBEm6w8nhVavVy5XOfuVAXyQxx8tZr+uNZvT5ppmvT6Na/BzvabSaH5l3mu9Mc9tZr3Gzxl3HzUaFS6c1td4Pf7PGfsL7OozPEayeGLuXhHgPbCF5/WtrQtEmHNAFhQyA+uwWCr/7nita3iuasMzJrxVvWbDmb2DaxivbqNgt7bqFwSDFzAjDrSg/XMzsA/cfYrn2mviBgf2Snit2XaN3wqI9gmAdecb69zl/AF+H5mkhIJS6rkyleaDSbLYSATg1Sf6HAq6CMV/xFr7htYack3XXOOvc/kSCh8JgcetVu0qB3jHyt//pM2QI0lRa7Wu6ms8d25ZarFDkNpJX0eESSgoKam/AXgnrbdMaxJg4sVp5iDQGgdyn+9MwSNWyuxHkzCIhmCr8k04mnU27mjSfHY/pZn282SCxk6YKi/sKhVdfK/f5LNGyxOz8m3vsvLK2rBrQrL1IZL0c7YtYIdodvrdUxJtDcDumD4SESZOUKi6iws7ab9hyqRAj7vtpX7aJ26NMlPQRX9FRzt9tMhB9Bmbzdq0KJV+QbPEndZtIkxywvyRGcIYglNOcOW6cH9Y9NdIZ9VSTqodCr1euVT2zRT7oLXjSpl/Z2qMlsNva3OlQmcVYrtCfOu1vSvKOa7uKl+uZ2U9MDhOJSQL/8dgCmTYGlHlZ04Y6dz6YfRM+aBSr1/GH8RzxTel0uJDTebAkX0L3NnFNSr8RnN6TBatUZhwH8g1l3CNw0Gu4W/xGX0TJENpvLe+xuXwFL9Xhto25+6DLBPGiPB6WqOmQBj2bxaiBIxa/DxI4E/NiZV7/Ygl7c9LvQZDa89rXzE1phBe5cQ6xl9qZx4dYf/errdsCgG/V4fpWTcxSmZWl9fatyaaMISEMvNNLO8ktQpEmAnHoPTDGRAGuv2iE0JmnNywHoaRnQ3Qwcx30npYeLNI8S0Gp3v+RJjsAuXbWC4vaV+sWBKPVxxeBZVXspPWw4ykFDzRxbc4MNFYJcKcL2C64K7NfvMjwCCtEJQyumiO8P+k9TAySRNghu76mWtJFsO3DNIKHV2INUgUWw8jwkxEFGQdRcNmVZw9GaAkqYeNwYc5PUpKdn/ClyL6e4dtGZEoKKyX9SHGoHrYGHyYWMJ8JIwPSTQ+kgW1jlkvC32dBPWw0ao/aRdtYLnuBzlPiNbUgqYyu1QqPfazu5JIOpROWg8bOWF0JxoJLAOEUTW1w6Dxq4A1LyyRKLPDO0IIr1Rifw5TDxvZ5irShjab9YsLRb6TdvGRYGRyOdvWNTAdUusamKi1bw5bDxuhZoEOd9264OLnPHecTXyYPoqboDe+wOB5ml12hHNEGAIRhjBmVM7pkBsJLwWo9AO8iY63EGEIZJJGjbzNPcft5dgUhbBOPlvP+vwe2ZrfTo+pOZ17xr1wZr2K7sU0RZbfRmD1sCAYlGQ+YUZWNzJhNhb7VnCqAbO0WZrfTo0seZx7jtuLuU5NVh4PypmVY0znzwn3vtdyrmFuC++VpfntVAiT1bnn/1ux77cXKdgNcy+6LdIs/PkEmhH7njd/U2dj1W8E3WH7VXJHmCzPPY+iYj9oL0F/Sk/3p2itVOQLOzjSEnnOw2H7VXJHmEmYe47bS3T/WpOYL9BpfSxn/RyZIExe555P3UuzeXGgOYp0xPUzR2f1HNklTM7mnuP2EjFHR6oPZa9gOsl9zK7fzT9sv0r+CJPDuedBezF8pF3UOo31ynX8/n5jqiGJpJ+CBFlcZI+yNL+dSpSUt7nnQXvRRFBONT6ve98Pu/1w2X5jkiosGwTXZ21+m9LdBCIMgQhDyAj+AwtGAyMlpWiYAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASMAAAA1CAYAAAAK2I0fAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAy6SURBVHja7V1Lcxy3EcYoVz+uskzsTfQ1HKyO8om1HFq2bht7doqXyNpKbbEmssnUHhhxqZsiUz7bykGiLknxkGscU7mLzA9QoscPMFc/QSYzDQx2MUMM5sGZ2QdbVV8VtYudQeMDGt0NoEHu3btHEAgEYtLARkAgEKiMEAgEYm6UUfDPQiLnt72R34sznma+4fxW63euP7iKHal67Gw4v2Ut/2tCTi3kd5753b+EyihnR/UYGzj+YAk7Uo0ddo3doKzzsGqFhPxOmt/6FdLMNtp6i25Sx/8WO1D98B36LW2tb1Zp0iO/k0OvBn7nRhlt9ZZtSuyjtcHgI+w8WqviUpUz22Cw9hEj9HC5t2VXxy87RH4nzi+bC2UEWlU0Gim90To2eUqY9wQ7ZlJHIq8I6zyu8j0eI0+I3XmaZwBdNH6r6PvAr03IS8LcJ3XwW6d1VJkiWndbN1ZY46+EsDdlznBi1iRvmbfzOSqfCcYWPPY557bfv5JtANkHWfrBvPCbR+bp5dfOxO9UKyOIKTQa5EVgGp2UrYzWW3SDEPo2S2BTtc6SZqmMZeT3lvxNksk8fl41ZnR6XaLf72s+0z0nrywD31niSsMdfFHmwJwXfosqoynjd5iF36l307i5zche2coo6zO73fYHHUYfBg16HDT4rxa1j1QtD0T0u90rUAa+l2Xava3F+ExtU+sIvqfM2+312rbjDj6F3wd/M0bpT9Kc5UvRzrVb/J105efu/fvvlR1LidWFQV0i7hmfAMiptCyC9nocyncKAWGoIzyHUfIcBj10tiKyhO97HbiDe2Uqo4L8vkvh992Y3/4n8TZl1DqMt6lskyal/4y3SYOQX9L4LaKMkuqiumeWid/W+obKrxXjN48sKr91uWozpYzu3+++5yyQZ2TBeWbqCAEZARfWsNF0fpB7VCAOoa7O3HWXbkIZIB2exZ9NyYH67NH7AkLgM5gtILAHszYsgcpODoMagn0eY9tV7Ykx1SVmWWwGbf5abXPh+tD/8XoH5vc1x7vjD9yrQWd7A88rIktWLvIMzAL8/gh1hMECfU3ld+CyLwS/7ll++/33dW3K99mUxG9eZWSqSxZ+G6TxX1hQKJXfWHuhMjqrrd+YOqsYeNZbNQAKAzcg64UkVsYl4kFS4SePXQQ5O6jLnECiKo/vXfsSzFkSzLom1yJmTptgGWQP6tJLrMuofWJy8Q4ctJnvL193vG9W1TZQB3BWWSKDR8NvXNZ+v/1xMDCftfv9j4P//2b8XdQ9yMHvUA3gwsDV8+tm5PcPf5Jt6pbEbyjzQdv3F0wyn+U3uS6hdaTjd4NQ56DXW/70DL+BtVSYX1BGGeOCF08ZhXEKk2vAV2ICYpI6szKIXsfrpYtXQPwLXJ8l9+7N1BnEMJuH5vQ76RImgTq9xL01sP/DCuuiU1pgDagmvCpvg608chy/HZ1h6VCVNass0XY8G99JkPXkjLwxZZGJX+hTJfKb1qbn5DdV5gL8nmTkd8PIb4q1M1ZG3JKyL6wySgo2pnVW+b06G+QpwxWZphN7jO5aBlIE8fXMIGFdhrq66Oo/shKUATwasJpBnVUWkzIq6rJUzq/oj2f4dcdtysrit2gAu8Pod0l10dW/GL92Nn4vujISQVryH/hd3KcdddaEWUqY4VHLQA1omsrEXTd1ZjLNjv3+2hWn2XxQ5cpDlroYXTRinbC1nRtxWeM7nPPIUqkymiS/MYuhKL95lFGWuhhdNOBXkVfnohXiN1RGdR3JmTplJH7DA23H8UZIiymMOqLS0GJ1ob0ofWkZN1C1fb/ffX9FDKzRO9db7LY6ewgTWRAjViP2eXzHc5zf+zv+ZRl8lCsVZbajqS7Rz0SnlO8fB0V1CkpYV0VlMcWMCisjuYJzHn55sLYCfmFg5uA333aGvPyepvG7YeQ3gyyRmFFNe6WmShnxzthYeZQaD0jorHJvBFlYedbudj8AV8/3nM+aTeeBLD/eoezuQRmxRAz1HHdUSQR1vG1ZxhWyvAJZONl25yk8W/6G71gN3gtL/4x522W1YVpdIm0dtEtvq70o3z/aC6SJMUBZ6Jyrq3S3iCyTWE2DQDVfyl9o/Ttoiw8z8PvhpPjNJfP5+B0a+L1VB78XUhmNGtLwzHDF4FhaV9cc/5ZOaYl9NqIMLO/7/s5ltR4QDIyUo+y5dBtFUDt4tud/ORoocNo5eK9cSi6rDTV1eafWRXYcEUAFeb078v3CSoh26tFgDZ9RVJYktzC5LPtXln6QhV++N4YHi/X88mVx2VacXzeN30ib9hLaBN6bld+sMpfA70vNittL+QwhS+OXvLLk4TfJ9UxbQaxFGUFFQMM7jPwDOhYE47JUSGh68wHY+PIsYjLQWV1lQLpZyO9U8Dssyq+yt+kUFFoW17YSQcKKxJY00w9uigYQm/PS4gp1blNHaHjgMYyzK1NlWILI73zwm1ehTaE2NiujkSmf4RgComIXvKKT9cjvfPA7UmgZt0TMpDIS5dhhnSeKEWPAErHuqEJpljUPVCO/s85v2gbVGVBG2eIQYbbBDUzYXj9gtcm0U7wM9JDfmeI3nh0BFJotjlJt6LIDaD+Tf5z37FTdykiY83QX8xrVP2GUuXXBPLPS75DfSfDrbudVRJC/TK4GwtGUdZd15F6nrBkDVJPqcdq5KXF2qrq8xEVWaHzHaePtEfUA3CfdUnqVQH6nm1/YUPqVTb/n+7g8/zPO2ehArnMAf2fNGDCzbhoCgZgswMJxYxtK+TgeZ7vIlTEAlRECgSg2XpUjKurnMr9S3owBoz/OGzMi2X+fmP7TtJqW9/kIBKI8xMdjUmYAmehOd4wkLWNAaTGjLL9VUUAZ/YpAICYGK4sXIzJsBu5YbNc1rK6tNpt/MWUMmC6zj5+roUd4FACBmPJgt8igcCIVCygeUFDNZvMHyLQa5t6+lCdjACojBAKRXxmJDApDkSZ3n2dPgJU4mYiu1Wr9sdmkf8uTMWCaIvOXeN6ZBnuEN4kiENMP2AcmsgzYz+WyvswSALeaKBkDvhopMUPGgKmxiCBdAfO82w5z/lxX/hQEAjE9mIpKQGR+hZKfddkdEQgEKqPzul1WXcdIEAgEKqNERQRnU3gCdEiuROhbane+h7Sa2OiICvpbZdeJI2ZcGYX3O8X3KZxC7uK6bqdEXAwoOa+fYHugMooA4j+rlP5dzbn7jeeshnmpT/GoBwKBqEUZwcYnZ23nevxz051XiPLc47QjNxnLROJ8arwvS16a8l0wU12i3+8nxCmTP6tPFsQE3DQdws1Qr3EPUTUQV/LQh/JmFIvaR+oZIBho/W73CpSRrjOUaff6n6jPEZdoWkf86A/zdiEXDewZgd/D34zSn+J5afg7lbw0ZQHqwqh1GK+L6p5Z4grp0SSnHGs6lYm9xHMg1w6VO4MTZYnn2EHMoTKCw3NV5kK6yAgGWzDWrGGj6fwo88TE2/uuu3QTysjNZrqbaceXAnb24DOeaCtMP6rc9pCal6Ysd1+tC79+SJMKVVxIefbKZ3lqHCxyuN7HH7hXxdU7nb26ZUFMkTIS1+2yQ7SKqmpba6gGcGHgBoPxhRy48audo67z+FqgcR6a3qZ0Z2CQqrxlyUujcZdyZ4EY1wWOG4gybqwuxiu9AyXr+8vX5U2zuiufs8qCmBNlBEc8IKCNZFdkcdrkqSnpuXIN9RkXObwGOXJHGWzhB9dnyb17U6codBZVgiX8eGx9mLJAJOdaTqtLuGp7ortRFVKfwuWIUQuKDhNz7KBbNt/KiPvhLfY1W9u5gY1dPmQaB3W2z1OGKzKNkoLc4laYv1j3THkYso7bO9xxXZjO9de5aNwKVBR0Uu6dumVBTEgZ8Y2P/JaBaJwoaQUHkR+mFUppSSSVibtuquVhysoHeWmcZvOBKS9NGX0nrS5GFy2WfVDnotUlC2LCykgoItZlrfWuGh+AFR88lV+BMlIGklg9ai/KWIm8Llq1cnh2BO66jc8CBnzdVq0D4QIJF06sNsXy0oTBZV1emvPCVJfoZ0LpyPePg946BSUsPa0shhw7iBlWRqFFtCmOgWhQ0S2kF1IZiZwyx5AfBo7agMKH3DHNpvNAuiPKDuU9KCO2AESTqEvrgzretiwjEq2zVzBxcFcmR16a8yCtLhEXLbCWelvtRfl+XfbBkYIKygbK59bqKt2tSxbEhJWRz3OYJAcsMX5UcnuLFaHjcJn6WHfVDF8WD++0gjKwZ8f3dy6rLg8Ee/lSvixH2XO51C3y0gTPVnbVg8UF79XlpTlXHCylLlLBiAA5yOvdke8XVmBUaY2UcfiMJFmScuwg5iBmhEAgEKiMEAgEKiMEAoEogv8DMH5kwWpcEhsAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPUAAAA1CAYAAACZWa3RAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAoySURBVHja7V3Nc9NGFF+HK7RXvtY36LV4nSPthXEUoNxcsDW5FPB0PBkVSDo+BHC4ZShwLvTAx6WdHHptC+md0D+Adgh/ACR/Qkiqt6uVV4q+ZcmS/A5vJrFkeffp/Xbf5z5y7949goSEVB1CJiAhIaiRkJAQ1EiTf9GE1JAP08FvfAFTImBGq/VtxxieQn5kT6tL2pesZVwjZH0GQY2UCaB1xoaaMTyD/MgR2AvsAmXdh4Ts1xDUSGOlxRZdpppxC3mRPxkavUVbi8t5q+LI/ArTSv9cg5LGm4Xh8Bjyw1OLmclSRR4OF44xQjfP9VcalQA1rE6CaWQGBWgyfOo2yAvC9GdVAF82gCPvCOtkyh+dkWek0X2R526dmaAudloX5lj9F0LYe9wp8ueT2KXJDtNXL5aZRwC+Bmm8KqsMrersIn+3g8HxUoMabIl6nbw1t6A9BLU/9TPkk2lLLxFCd6I4yFRtwWtXDLs+UmU51eR3/NTc0fPCVd+koA4fz+j6uut/v2ckmcvQ0M6Yi+s26wy/qYRN3WXkOYJ6MnyK+sxer/1Zl9GHpuB9NIXzU42aNri1q4DADnq943Adrsnr7f7gC7dWwGhtE65Tpj/o99tM6wy/gu/D34zSP6UKysNr2uxV/nt07mVvbe3wuEHtNx5V7RYLKdkHTcbk1VNrfvu0tbgEYxTPIK9r5sIIgJRzaVL6h3sudUI++M3F+r0twrrPEdQI6sS0ttY7rJ0kG+SkthEEGlNwTbmtbdeb2mMZw4axgLccBPZO58wluE5Z5wE8hz+Xklf8uYPBEcdvmUIL9/AYLaGboCFAWMd8zq4ADN05119hOmN348TL44I6aDwuTWbZ5PmWfC6AuE7q//JxmyrzrKbfMIadUyYg38Ozks4l6rtAUCOooziB3gcJkrC5a9uqowgAYAr2WxBsaZO7HW3CRhyp9XInoq2+HboBYVfnYuizl0EFJeYuH2YOuFThmcGgfQJA3R4MTpj/Hxpd81F37fF8/6McT8c1Hps/ytw4yE1+Gca5s5p+c171S8DunWQuDlDnaFcjqKsIamHH7QSpfNwzTrVXXqBXBHHLPSYvWx18A6DOnuncueTl5XXs8CG7laUK70p136I91/+fgrzWYeMZdhio03vSiSjnW2dzTzTNaDt3c7qtzjXOXJy8jObfqCyopy0UloRPQTwKA7W8ru5AUa/zxcAD7DqjD0z7cxvUUn/HXfzdKqmjrBMwHovfDtWb80tZ5Gwweix8ceaCoLYYbHL4H/jetOQqx+WTxaM3fjyyQe2zmwgVWjiJPBaLmt91t0qu7oJe9rakwWDhuNZs3k/iBY4D6ijj8VW9SW1Pna+X6p1kLghq+zvcGfFxWvKV4/IpjEdhNrUNWkUohce3fRrsSWk3q5lQg0HvyJwQTvs3F1vsurpbCbVWCK/wDq/zcJCuad8Zq8ZR6cCSnuNxgzpoPM7PBIBhDCPHmtN3IFVv4IHnXGDBiDAXh02dkxlaKGHlwlife5KXl7CMoI7CozCPKzjEeEjp5NxGu9f7DNR4Q9fON5vafbhfybZ6bl7/XIS9YIwjQMudkGr6XXgG3NMR83gH8+AqaqP7Ap4rv8Ozq8zf7PfbDcb0u+MEddh4HLw2+dJfaZ+GMUitRt2lVf6ZIL46P08fJJ3L1Hu/8wS1M6FifaZKoLaFLuCZlhf3o9zxZzXjqhv4EKcVTiv6EcJahrF6VB0HOJUAFPZ9lL2W5gA4q/hzdeOy/UyoXDJ/U4bIIssEYX+F8SZsPBJgwhEH89Vv8JAXD1U5gW8vatb3xVzqH9xzgfh02Fy81P2sZTQzwMBKqTHyOwgWOCsiZQ/xVdO/AGGcedJW3JEnHEwqPzoJn8J45JxffnYcUtD7Mu3vBOm6SWU0k4kog1FCEN2n0RhA//MSxCzypL1UrzzJmdAQjU9BPPLYIbbyTE9E8ngP3IY/GC3IclEo4KrmLbBZ5JNbDB/Ls/IKwUUFta2C55ieiORjWqXQBJMsCqUBdVI7PZDhAQkYscadYyVRHFALhxjbzLNCCGlEEP7ySlGNvSjElNEi2h+B6nCKhJaaM/0QGE7ey1NBJlFJlIfJ0BenbyzhwYP5E0QAqNa/lUZGGyCj1vuLKqP2H+6c2wCqlQ3UvMLmcusio4RX7kABw2JntiMdSWolkbw/60qiPP0AkF1V9rrq0tnS4IWPGLZTfUaWjO5Cyupih3VlrDxOhZgKlqcHnFselOV5V1mAGpImug36iMdYrUR9K5zD0wLh79H8RMJF1pVEeYNa+CS0Np4mmg+B2eMOEYbJ6BVbRo3zPjIauUKs0uo3rGZXeK6yM/NKxg7VBWrExMSVRBtRK4kmAWqkYlKojCaoEKs0qO2UwIXVC+rnIq/X6WxKUEn0KbySKDyMh6CecjVdSVt1y6is7/aUUVd+fSY2NYn+/ZDqovF4v/2qbGD83OvtAV67+iamGh2z6CAVn8J4FPf5SPlSZBm10lm9ZbQRWCE2Nps6yndVyhrUfjsarIxexf9K9c1OxpVEu2n4FAHUu3HfBVJ+NCYZDawQK5YqwsFB3yQFtRISOFA+CJ8BE5vN5mPJSGn3WtU3V9VKIvmdwjnKIvAIqSQONSGjexKgioz+LDcXl4xGqhArDaij5Ekb+uwVeXicTK+zOiTwKiTwSEoVu9Vq/dBs0l/zrCQaF4/SJjQgFcdLLmSUH700Nhktkhdwhtfs1tkTL3BEySeX4SlpIsBpHPw+yl7b4SyrekhbWD1rBFYS6WOvJMqaR0jloy6jP8mKMhnOklVhcAJqkgqxwuzQ4L5nun5dY9rtaaunRh4hjXXxL8IgwAs4R8nLaTrtBHmEVCpQu3NYMe8Y+YRUYlCLHFbW5S55KO4mdIc2uo/giBlkOPKpYO9g4qfelALU1pnK7vjcPjnZ+jsoC2bqbGTkUxF8FJl3vSw9qMHum6f0N9VTd1PX5q2zsPYxtRH5hFQyUENsGEJF7s+DzpmeRoL4ZJH4FLGrZeLOl2lq1dOp1pPvelkJ9duLrGD6FsZWi8enoK6XUmhTdL78Om3XyyRUpK6XlQW17KSIwC0Wn4K6Xqq2f+LOlxq7nbbrZRLTpkhdLysJalHmyDZxl47Ep9d58Sms6+XonvSdL9N0vYxbLVi0rpeVAzWkNIJDCJMlisensEMXx9n5cgxdLz2qBf3P/ipS18tKgZrbGy12zX1AAdLk+RTW9TLsniSdL5N2vUxKRel6WRlQ88QKfpKi0z6cpva0ReZTWNfLoHuSdL5M0/UyLj/DxpJ318tKgFoIKuux1mJPtYHAy4rVRQf4dN3i06E8+RTW9ZLfY7XtSdr5UnSLTN/1Mg4Vsetl6UFt7TzLIu3RgybUs6qIgO5PkE9hXS+VHS1x58s0nSKTUFG7XpYe1KI+2d+5gfb1yJET5AzKg09hXS8l+JN2vhxX18vIfoKCdr2slKMMCQkJQY2EhISgRkJCctP//ic1sCmaW6kAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
Let cosx - sinx = t
⇒ (-sinx-cosx)dx = dt
Therefore, I = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 34.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let tanx = t
⇒ sec2x dx = dt
⇒ I = ![](data:image/png;base64,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)
= 2
+C
= 2
+ C
Question 35.Integrate the functions.
![](data:image/png;base64,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)
Answer:let 1 + log x = t
⇒
= dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 36.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let (x+logx) = t
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAAAxCAYAAAAm0WAHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAdRSURBVHja7Vy9b9tGFD/aHZN6TRwdu6Rtxognjd0c5hw7ATwQLkVwSVIiEAS2jlJwMFzKm4s07dxmsJ0xQ6cGTWJ7aYc0+QMyJPEf4I//IB/qPZInURQlU6I+KPgMPFiQbeje4+9+7/feuzNaX19HwoQNy0QQhAmACRMAEyZstABjX9JjhKYQ0qZFoAXABmoArPKyuniFyA8RIvum654XwRYAG5hVKF6RZfRaQuiTAJgA2NCsRNC2AJgAmACYMAEwYfFalxVT04FJAmDCBlqlV1RcZd/fSwgfzpVXiQCYsIFZrUovF2nlFry2Kb6LiLElACZsOGAzyCKmlRUBsARWZ9SfVT0xrlSIUF3q9DPL0mZUVf8OocdTAmAJRKtNqWZW3YsCXM1USFT7dhyA4GcyQgcMgR+xWrknAHYCuAxCXFqtXRYVWqu5JlnARH/QiaXKoMEw3bE2Ns6cCoDVOXUT9CdCyv6c5RS6UXhQEd3DtHw3K4Fhm2MTmAEhfExtNz/u9QCIgKXiwO445mxBpr+PCmCBjJlumjaNAmkTTedD23Hswz60GCltdvr91fIcwYi8zFox4OrkOmPgd1lYl+ua5wnCL3k7Isywq3rx+ihEPieOsl7UMcb/QovEe7aY/LdkVS851lwB0vnIUmRSEVtS0KNhl9laH6c6RrGuXswgaAsppUfwGua9jQfcZfMOKh4A6Ds6KWEkHSGsvNCr1YaUcavmRYLQW/Yo68SsLWQKYIy9FIzQMTFqi8Pc/QpSdnphIkg7CpL2owEbdzsCJIfpOLOjjAcw1x0V/8i+fcKkdD8uFde8rNXO9mMPGmivJDoHmE7zUkJTyzW1QPfd2A/AuqXH1gJAiy0CIkXCdJs26cMf16Z5bzPq7vVRAmxNz99g66ojom91TeHy1T+i4OsSkE422H5LkkrTz/1LBQXjp5Ai+GFGmxZvQZnOKqhn3QRuPwCLS4+wDsc0L5QIfsC1pYTzr7Sy83UL+1na58sqqTIwHPq/Jx8Q9Y7FXn/G49iPP74OQ+9YStweFcB8Jkf7jASOupGAtzZirHWsIqFqahPmMTZIMbmxYZ2hObSLcnS3K0CCooFXdSB0DUJ+Stov6xVgcekRQAA7GTQITxOw/nmMnrP171mOc9bzybHOqjm0x9Z5SI2Ved6vYmA7ghTjxRDjf/wZYqs/uu1+OYh4DTIePpMDe/WnRTNQGbHdkTBgtlFc9h4UVl5165dF2di2tVwe5Xc1284lYeO49OhXutJxVFD7uqiZ4v2Uj+phTRkAYy/qZ4s/CVohDYD1OB1JEw8/w7T6MzkACzRFUsr3AozRzkmAjGNjKWCPJK2TaHp0GCt5AInRZFEN6VV6PispnPl8cDI/8fzz8LqT+tMOsN56c0E83vcaj34/bygaLNnf+tYvwIIHWu21kupHc2Bq342uM/xeS4slBDxI55D6uOaqWkuXaE7a9XSY6S6k8WcQD7yXeDQ2QGjD9A2wtBosyd9yawNYwh0MD3++UPgZ0kovlVTvmsMXtLw69NNge5poMFNEn9gquc3S6SH3V5bJkzh91as/owZYk5FRPa+v3ehW4Xcap2Veg/nM+hjYVTIovWnX7HNekBnr+Y6dXNX2ElCPkTDd8T6HGjd5j0cKxHi4UvTFvHwQ1oPe2EsnJVZRuXE+pfGnXw2WasMFjIxy6p5mOTNRIIE/0MukZu2bzAEsSVXkpRBWytsGvcYfpLermMPlsqbElcb9BpQDHmZ+rq7nG2nPf//tlPLtI82yZmBcopOp7Si4Qqx8hJXl30zTuRDtlaXxZxxVZGhq8EFixQiMhHi7xbGsWah++cHHzAGsScGdd6TvnHxQNCrL4V0F/aJOXeUOAX16IsCq5kWmv95AHyraAoFWg4LRC97Xgs+27dq5aJ9stax9RWT5r5Co/oix8veSZRWg2ZrGnwbjpxxfJY1H2FYMOh/xq2PqzxTAePrJwomFNOaPU4hVpHZjN9ds+xykQSbUXsAd0bTjMJ8dpeMsja8y3aYId6fTjj/GvlGCOaHmuBfaxDzTa1BJpgVGlk53jBVgzTlb/BwuJk1u8lMCk2p82oCV0q+g07jvMFoyKHZlufAkLTC8picxNicpLkMBF1QVJNArLP0d+T2hziDzRynkpenUZicZZHE6Bcny6yLVf0h7GBBaGnAeLCsnfscGMABX8ZrxPZ/Vsd275umPE1IgiN8v1Er1JLY7jcbvQGb15tDIAAaAMqmpxZbWCSqfEsH3QQiLW0UxGSFBO+ZUinyY413F0k7S3VcRt4ra5EO3PtOpBlidD3qJ8YsAyyll4KExl6XN+Ge48Rt1ubyY1YuhwiYQYH6nGL1pHhJE9axeDBU2wSkSOtkg3MV/OhQAG6rxQ3iTPg4SllGABceKjyatSSgsYwBDjWtX/nkn/p537SlyXFiYAFjvTBXcnpHJlYfBuaHpiq4uwDVzwV4CYKktOMP9rHk8Ov7clDABMGHCBMCECYAJO+X2PyPQVkgA79LhAAAAAElFTkSuQmCC)
Question 37.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x4 = t
⇒ 4 x3 dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let tan-1 = v
⇒ ![](data:image/png;base64,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)
Thus, we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 38.Choose the correct answer:
![](data:image/png;base64,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)
A. 10x – x10 + C
B. 10x + x10 + C
C. (10x – x10)–1 + C
D. log (10x + x10) + C
Answer:Let x10 + 10x = t
⇒ (10x9 + 10x loge10)dx = dt
⇒ ![](data:image/png;base64,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)
= log t + C
= log(x10 + 10x) + C
Question 39.
equals
A. tan x + cot x + C B. tan x – cot x + C
C. tan x cot x + C D. tan x – cot 2x + C
Answer:Let I = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= tanx – cotx + C
Integrate the functions.
Answer:
Let 1+x2 = t
⇒ 2x dx = dt
Now,
= log|t| + C
= log|1+x2| + C
= log(1+x2) + C
Question 2.
Integrate the functions.
Answer:
Let log|x| = t
Now,
⇒
⇒
Question 3.
Integrate the functions.
Answer:
let 1+logx =t
= log|t| + C
= log | 1+ logx| + C
Question 4.
Integrate the functions.
sin x sin (cos x)
Answer:
Let cosx = t
⇒ -sinxdx = dt
⇒
=-[-cost] + C
= cost + C
= cos(cosx) + C
Question 5.
Integrate the functions.
sin (ax + b) cos (ax + b)
Answer:
Let I = ∫sin (ax + b) cos (ax + b) dx
We know that,
sin 2A = 2sinA.cosA
Therefore,
sin (ax + b) cos (ax + b) =
Let 2(ax+b) = t
⇒ 2adx = dt
⇒
=
Question 6.
Integrate the functions.
Answer:
Let ax + b =t
⇒ adx = dt
Question 7.
Integrate the functions.
Answer:
Let (x +2) = t
⇒ dx = dt
Question 8.
Integrate the functions.
Answer:
Let 1 +2x2 =t
⇒ 4xdx = dt
⇒
⇒
⇒
⇒
Question 9.
Integrate the functions.
Answer:
Let x2 + x+ 1= t
Differentiating both sides, we get,
⇒ (2x + 1)dx = t dt
Therefore,
⇒
⇒
⇒
⇒
Question 10.
Integrate the functions.
Answer:
Now, Let
⇒
⇒
= 2log|t| + C
= 2log|| + C
Question 11.
Integrate the functions.
Answer:
Let x+ 4 = t
⇒ dx = dt
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
Question 12.
Integrate the functions.
Answer:
Let x3 -1 = t
⇒ 3x2dx = dt
⇒
⇒
⇒
⇒
⇒
⇒
Question 13.
Integrate the functions.
Answer:
Let 2 +3x3 = 1
⇒ 9x2 dx = dt
⇒
⇒
⇒
⇒
Question 14.
Integrate the functions.
Answer:
Let log x = t
⇒
⇒
⇒
⇒
Question 15.
Integrate the functions.
Answer:
Let 9 – 4x2 = t
⇒ -8xdx = dt
⇒
⇒
⇒
Question 16.
Integrate the functions.
Answer:
Let 2x +3 =t
⇒ 2dx = dt
⇒
⇒
⇒
Question 17.
Integrate the functions.
Answer:
Let x2 = t
⇒ 2xdx = dt
⇒
⇒
⇒
⇒
⇒
Question 18.
Integrate the functions.
Answer:
let tan-1 x = t
⇒
⇒
= et + C
=
Question 19.
Integrate the functions.
Answer:
We have,
Dividing numerator and denominator by ex, we get,
Let ex + e-x = t
Differentiating both sides, we get,
Now the integral becomes,
= log |t| +C
= log|ex + e-x| + C
Question 20.
Integrate the functions.
Answer:
Let
⇒
⇒
⇒
⇒
⇒
= log |t| +C
= log|
| + C
Question 21.
Integrate the functions.
tan2 (2x – 3)
Answer:
tan2 (2x – 3) = sec2 (2x – 3) – 1
Let 2x -3 = t
⇒ 2dx = dt
⇒
⇒
⇒
⇒ 1/2 tan t - t + C
⇒ 1/2 tan (2x - 3) - (2x - 3) + C
Question 22.
Integrate the functions.
sec2 (7 – 4x)
Answer:
Let 7 – 4x = t
⇒ -4dx = dt
⇒
⇒
⇒
Question 23.
Integrate the functions.
Answer:
let sin-1 x =t
⇒
⇒
⇒
⇒
Question 24.
Integrate the functions.
Answer:
let 3cosx + 2sinx = t
(-3sinx + 2cosx)dx = dt
⇒
⇒
⇒
⇒
Question 25.
Integrate the functions.
Answer:
Let (1 – tanx) = t
⇒ -sec2xdx = dt
⇒
⇒
⇒
Question 26.
Integrate the functions.
Answer:
Let
⇒
⇒
= 2sint + C
= 2sin + C
Question 27.
Integrate the functions.
Answer:
Let sin2x = t
⇒ 2cos2xdx = dt
.
⇒
⇒
Question 28.
Integrate the functions.
Answer:
Let 1 + sinx = t
⇒ cosx dx = dt
⇒
⇒
⇒
⇒
Question 29.
Integrate the functions.
cot x log sin x
Answer:
Let Log sinx = t
⇒
⇒ cotx dx = dt
⇒
⇒
⇒
Question 30.
Integrate the functions.
Answer:
Let 1+ cosx = t
⇒ -sinx dx = dt
⇒
= - log|t| + C
= -log|1 + cosx| + C
Question 31.
Integrate the functions.
Answer:
Let 1 + cosx = t
⇒ -sinx dx = dt
⇒
⇒
⇒
⇒
Question 32.
Integrate the functions.
Answer:
Let I =
⇒
⇒
⇒
⇒
⇒
⇒
Let sinx + cosx = t
⇒ (cosx-sinx)dx = dt
Therefore, I =
⇒
⇒
Question 33.
Integrate the functions.
Answer:
Let I =
⇒
⇒
⇒
⇒
⇒
⇒
⇒
Let cosx - sinx = t
⇒ (-sinx-cosx)dx = dt
Therefore, I =
⇒
⇒
Question 34.
Integrate the functions.
Answer:
Let I =
⇒
⇒
⇒
Let tanx = t
⇒ sec2x dx = dt
⇒ I =
= 2+C
= 2 + C
Question 35.
Integrate the functions.
Answer:
let 1 + log x = t
⇒ = dt
⇒
⇒
⇒
Question 36.
Integrate the functions.
Answer:
Let (x+logx) = t
⇒
⇒
⇒
⇒
Question 37.
Integrate the functions.
Answer:
Let x4 = t
⇒ 4 x3 dx = dt
⇒
⇒
Let tan-1 = v
⇒
Thus, we get,
⇒
⇒
⇒
⇒
Question 38.
Choose the correct answer:
A. 10x – x10 + C
B. 10x + x10 + C
C. (10x – x10)–1 + C
D. log (10x + x10) + C
Answer:
Let x10 + 10x = t
⇒ (10x9 + 10x loge10)dx = dt
⇒
= log t + C
= log(x10 + 10x) + C
Question 39.
equals
A. tan x + cot x + C B. tan x – cot x + C
C. tan x cot x + C D. tan x – cot 2x + C
Answer:
Let I =
⇒
⇒
⇒
= tanx – cotx + C
Exercise 7.3
Question 1.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 2.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiwAAAA4CAYAAADer6NNAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA/WSURBVHja7Z3PkxPHFcdnOds++eAftE7BTvkU1LvHUD5Q2gGTVOWwgDS1lyzecinUVBlwqVzE1nKjEsg5kEMCh0BS5RztlCF34B8IhOWYQ3b3X2DJ9PT0TE+re6ZbGmlb0vfwKZcXafT0Xqv7O69fvwlu3LgRAAAAAAD4DJwAAAAAAAgWAAAAAAAIFgAAAABAsAAAFo/hcPN9GgS7QRC8GYUchPHwJPwEABD0Q3JlJQhe6+YM0vniq+Q/KxAsAICpCJZ20H60ORy+D38AAMZlZ5N+RjqXr0KwAAAgWAAAECwQLABAsMAfAAAIFgDAwgiWOArPrtPW3SCgrzYHgw/gRwAABAsAwCvBcrlDrrZawXNeZAfBAgCAYAEAeChYBD0a3INgAQBAsAAAIFgAABAsECwAAAgWAAAECwAAggUAAMECwQIAgGABAECwiMksDk+2SfCMTUzdeHgCQQFLtZgvwfiftWC5eXP7rR4ltwPaS94frGCcAeAP7Pd5hpAHhPZub2wP3pkrwcInJTxTBCwnyzD+ZylY2GQYkuARCaPh9s2bb2GMAeCnaEluKn6/QsJHLqLlSAVL+lC01vpdTCxgGVmW8T9LwcJ6uATHw8fbg8Hbvvkh7nTOL3sWmWUUaSe+tOiZrzgMN5Y91jtXw5+thfGWKdZMtKyT4EfS6V+zFSAQLABAsCyEYBFPhWYTmm8+iCj9FhlkadGhvduLKlpYrE/3r7cRaxHr6FYQ/P2Y7t/5U5np7sZg8KH/giVR2yRoP8MzRsBM7nqi8CyrF/FlQVuW8T+OYEm3dlaD75hgsZ38uT+Dfd8EC8v68EkW9TRFBoJcWUSfLOr3moR+7pNRkcEFC9lPfuPUxme2guXLKDxDSfDEJXtjKVjIC1/uPOJo7WIy4R2ImgJ2FzCvd7/Z5H1Ao51z8ygsVgn5IY0DS+83EIN0qyCNa/DGL8Gy+OPfVbDsRPRcYsOhiFcK7d2bR8HCbaJPbbJEwn7aHf7C09/k92lcGthy49kw8nSRMhFjxHqPxdo3ccMW+yLW6483trffaSDWT3SiZBqChV8zeM3n+i++WkjBkk2Sb0ZoaMGcJend6fHgMbN/ngRLYTdfLON4571piDgIFkuR0ND4n9XTmsWC79PpoIgGf7GxRxQLp79ZjwRLYVcmYLebi6Gtb+aFrnusD30SLKKmhAkI0u79oclY92jw52O0e0/dGmJ/n0aGhdXPMEG4kBkWPoDI39ai+KJ8RyHuNuctS8EWn3mzPas/eDXN470QLM7jf7+JMTQrwZIvBJ4sgi4Zk+w3uz9NwcJ/Y/RH15og9pvc6F//qPF5Kll8kmvvWmUkHG0/olhbZUzSRVeKtRdjlcf6JY/14ONpxVqtVeGCpfkalikKlqPftmB2hN3hKVPWZZ4ECxt4q2T14eYmvTQvtsuZlWku3n4KlsUf/7MSLL7dtfNtyPTusW3xm32Q/WYPfRAscmZlWts2sqCri5fvgoXVrmSxpjaxjiL6uS8ZFjmzUmf/2IIlExAnu9/8Uv6+pszL3AqWYdw9wRtr8RR1i46eqmCvyWseGKT9TF340kkzuw67Rhx3T1IaDesnHPpKTLTCXjldHg+7J3hmgP9N/S519jdtO2uYxWzQLTa+2i9srRISE9ue2BXFPGvGPmec6x2FYPFw/O9rfLZb5bNZCxbTOGJ+oiR4WvKlUouR+fL7fHss8aW6YKeLZ3Yddo1+f6PNfKkuPKl4sjjlFFFyS/rNlgSLzuf96xsflXxuKXBcFn1hS+LLa6YFdVLb8gyOhcB0zg4VsT7M4vSnCWN9yK6RxfpbQ6xrMwW6WItriSyNxp8vZX82LXB49iN4XRVrIQAK2zr/Um1TxYg2g9O+eF8WJ6ze5FgafzvBwgSOzgdZvJ+ksUzieKHfOScEy/X+6faI7YONj5k9K7ntX4/Y7jxh8zQpeRFG8dnSoiXtq6t3zfIEL1+XHZFk5/+FokyPTNYU8rHXqJOfrj6EDz5yIOy0tb9p29PPo73bVXfHvtlf2ENfhVG4VSzO5EC8Zxzbq2wTf3O5nm5saGueFGxE2NyNf6XWIvPZvslnM90Saq3e0X0Os7EVtJ4rvtyXC0jVol1Z4MgLL1ucZF/qsjq5n2oKVMVvlr1XJ1jqfN7pXv6s6QxL8Xn0VafbuVQs/Ow3eflz7feUFlNb22x9NI7YYrFmn8/sqYn1Nf6aItbywitizf5/4ljnR3wTH3GRMJJh4V1gWbYjOBR28NeSPfF9mv7N8M+zi7XRtgv9c1W25e9VinhTIUTOPLQt7NUJFiH0RDZFFi+i6LbIItnb7jRhi8VEnjDzltvJwGCTUr7gKIWBxd0zvzsU9RGlbAP7W8UdZtWR06Leghx0NjfPp1swyuvq7O8O4xNN2p5vBWV2VKXzfbI/tyVRxd04PllaUDULvovt6oKsy+TYXO8oMix+jH/6tGL876Y+i6ILdT6bhWBhk1S42rpj9CXrfqv4kt3tpr5MFkHTolNkEXimRHz3UhaE+7J01537qGIRy7eCskXYJFgMPn/guj1iu+jnn5X8Jjf6/XZJmGmyLuPaJgsjO5vsxZZ8tDiPNQkfWcR6L63jGAw+FFmBUhbEHOuXTrE2CJbS9SaItduYSD5LiTWvLTHGWth20SXWQhipWSgh5Gw63qqCRQgRdVupyBoVp4Qy2/+zItlelRFzmrDt0uXZxKwsTGpNhHwnzVK4dUWdogixqp6iWBT0dRd19jdtO0vfy59VV3/gi/2muhK5CFdd6GxtH7lmzd9n3R5/Acb/vk2Nw7QFS90RWZviV9MJI7WWQ84oMF+ailFtTiwZfrPGGhYXnxfbFJqTXyqKjWr2YVSYjAoMV9t0vm3S9qqtk9zWdu9+XazZIiu2g2pivadeT4bVuLBYi3+vEixl8ZTaUltXIgRGfca3f02fnTAJE43AyLeH7GwrCxb+HvU780Jk+qRuS00VLKZalbq/BwY7LASL/pSETcFffhRZk9oWd+ji/WotgG6fPx9cHXrJpn4hvds1pP3r7G/S9tSP2VaQi/98sL+qEJZfRy8ixrG9+rPM15uuYJnd+JfrN6Y9/l0Fi9XiVGZFzbCcIeShzu46ISC/RicwssUz347R+XKk9qFGsIjfrPxvurqGURFCbtXVlkycYTEIlsIXelHiaptLYa+t7XVCQH6NTmAIoSTer9bCVMTaKFh4rPlWkBrrqrqPSWLteNO0p/sM+cix+r5uYtuKtOUyiWBhNqyuhr+zOYk2IliyTIrqx6qi2/QZRnn2xVw74zRhm+4eta/R9IowLXZsAK7T1l0+2YzevYuulFaBTiacKCTDqsXRZH+TtstN0fToruWH/XkmRfM5atGnre2mIt7KDEvF9Qw/nIZqWBZk/NcUV86kD4vYFjXd/VdkO3R1DnWLtNiG4otZOetQdT1xx10t0nSfxxe+zOfOp4mct4Q0/uJ2jx5F1tlm34+kOcFiyp44xnq/LtZyJiAXLJPFmlb5s0rYNLIlpBTDyrFWsx7j2CYJllLPlew3+1fbY80mwaIKJ5NgkW1fyYWOXnAZJjKivdMrtgSSSV958qq4AzQ1SFP39tn/d2jnG/kaujvY9LqaQs/1Fr0rT7ZyvYjpSG6d/aznRZO2u9yh+2Z//swYZUHTFYY62W6o7VBrWOquN80Ftmb8787F+K9ZdI76lJDsy+Nhb0deVEq+1DRuU+sdcl9K19Ce7rGoYXHJBMk1EOMeOXYpXDWdcNIVnY5r2zRqWIqtDE2sw7UtXazlegg11iENf1uKtSaDY1PD4pIJUv3Jt6Xst19cMfVCYY3w1NoQITBk21YstldMNSyTnhISvufFvEUNTJE5KrIosjgqHeXeHqzaFd1WTNillHdF983iNUXDsaz/Qb7o5AWMUqtx1obcOkshLZq6/X25yFGuD6izvynbXQSLj/brBIZ6HVfb83gmsROLNsss5EeZV8Pv4p34PdvrzVqwlLYp6sf/odzc6yjHvy6t60MflkpfZotMhS/zO+68qJP5Mntf5stS1sHlBEydYOGTPXkoCwC5GNi2qZuLYNEJLqnXSLsJ26Z2Skhs+VTFOrszF43S2HhRv58h1hfUrMNYsa48JaT15960mroVgqs4wdPX9JWRbRs9il1tm+mUkGsfFt0pobwVf/vifSZa+HPIWn/Mj9zTzj+2B9sfJPPWg1J2J7e9/epX21d/WnusWXf3NpJOYx03SfBC7p2gK9yUayQIWf1Bfk36BcJoK45P/1zuyyEm3botFfV4qLzNMtLPQ71rrbF/UttdBYuv9gtBYbrOWLYnd8/5v7OeIYkNbAtmLYy+ZAu36/WaxrPxf2gz/kU9h+Kz/Sqf+dLplvmy1Qqe1/lSrk9hvpQXXdmX+es0dQ1VWQpXwVIUoPKshdbnFttDrr1Mson/jhgbqi8mtW2afVjY83CyWOd9WFTbpVgfVsT611KsD+ti7dKxlQkmdfEtimd51mKkN8uUerGIRb7wBf2n6i8b20zbQ6atp/SaSnbEVbCkc1i4tpXbwvqs9E+fagWtf9Owe4WJSJ3trSD4X9n2ci+Wke0eurl5SU1VA7DoLNv4Hw4//eTd4N3/fjocfjIDv+760ulW9CNZpAf8NRovh063vpP19Jhap9gFibW2061La/7oJ8HDt+lvbttmZCahrOZmWCsAgE8s2/ifmWDx7GnNup4tQBV0ds8SmpObkJeLIL6mJ+joS1WYuD6t+UgECwBgie6ullSwpBPsgj2RGL4x00WsjZhqVSBYAABzL1hYIWtRT0QO5MLHeRIsecfgBcgiNJ+RMDf7m8vvlMXadntjyWL9xNQwjrXHh2ABAMylYLE50aND14LfB9jpE7lVPFhcnyDWo/Rzn4z2O0kzLCR8ZPssIQgWAIA3gkUcnWR9fvJFIEqfsr1vcxomFTsOx0tnhXhKL8ZDdjpH88TjRSGNNWpZamMteqG4+AqCBQDgjWBhE1zYHZ7SChF25Ldm0ZefqOubaIk7nfPT7u0zFwtY9vTjRf6ecRhuLHusWbfZtTDeMokVJuz44ynsxQcECwDAG8FiIn9Mg+WTYcVkCP8D4BdZFvVB2g/L8aYCggUA4L1gYU3+fKtNAQDMFggWAIDXgiU/aTOD1v4AAAgWCBYAIFicBYsowkWDSQAABAsAYMqCZfxnCYmnKcOPAADWt8V0RBqCBQBwZIKFFdqibgUAAMECAPBWsKSZFeX4q83TrQEAECwQLACAmQgWfoRZ6XIroL178CkAECwQLACAIxUsmVg5NAkW1LMAAMECwQIAOHLBAgAAECwAAAgWAAAECwQLAKBSsFi01QcAAAgWAMCRCRYaBLv6uhRygKZwAACZfkiurATBa92cQTr9axAsAAAAAAAQLAAAAACAYAEAAAAAaID/A/W9Oa+YinZNAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 3.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 4.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:Let I = sin3(2x+1)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let cos (2x+1) = t
=> -2sin(2x+1)dx = dt
=> sin(2x+1)dx = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 5.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let cosx = t
⇒ -sinx.dx = dt
⇒ I ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 6.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
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⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 7.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANAAAAA4CAYAAACMs3abAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAZ/SURBVHja7Z2/b9tGFMevc5MtQ2PkNNUdslknjS0yBDJhpGPb0KymGB4Cl0CQgUPQ0t481H9APTVbW6BrhiT/QPwXtIA9dpL+Brs8ihRP1JG842/pvgHeEEESxe97H957x8dncnZ2RmAwWDmDCDAYAILBDAco+PdZlsFRhgbnBsRDL36E708fMkJuAnFu143OLNffQ0CZZScT+loeD+SOTk5eA6AUQEMy/DD1/YcIHlienTrsGQBqASCkftuphXEAqTivboAOGb0ghN3Yrr9rehDWoUXRubdZnxgDkOtYB/tscMmdVwRGQwBd1wWQ71p7lJA5c06fbShApbRQ8aHrjJ9zbXhtEtSrc8oOL4497z4AqlgADgbkn4Wo7QNUp52fH9+zHpGP/Fw2EaAmfciDOV3gh/bI+nh8fn4PAFW++pG3mw5Q6LDoCmsSQEU+DC8slP45dtzn4ooVaDVrUisAVBNAVfNt1dpsREd/TKfsKB0Usry/q3sVVY5X9NksH/K01rL9bzJWpca0AkAVAQrfS8kVTxkGbP/Sde09xhw/cay9y/N2SoZX8ffxq6VjjV/x12zf3V3UBUHKQYdXefeY+Pt4IKSDIqqJZmLK4vr2bnQv666t1UpXizI6qPpQTP3E9+dodV1GKwBUESD+nWziHsVghMdgh2/j70kckxx38TsWRe7Ycl7x/DzeGIg/K3VUUBBnXVVltdHifXRmOe5BW+mVjhZldNAFiL8/HeCLdI98CLWy/W+raAWAKgAUdyyIgRy+Jlx1s46bfm0JgKTgXaZu0XtlAK0GKZ1PptPvxc+0sfqEWkQBqaqFjg66AC1gZJ9k713RynF+KKsVAKoAkHjV5ynLdy/ffKV6XJ3A4WmICEsWQEKKMueB0WbLkUwLWT3RFkDxpkKeBnVoBYCq1kBBXh/n/WE6IsnfqwAUOjlI3cQiVwRIHqRhLdF6jxbXglHySUeLpgByJ+xIpZapqhUAqmkXLi6QZfcpqgCU0cR4l9hqc2sMnGNRv6utbh0tmgCIa6YS1GtaCeknAGophZuwyc+io2XpVdUUTmVrNl0rJSkVnT99+WbYRgpXRou6AQpXnol7JK7Ynnd8f3/ALsXPrGkVbiroa2UMQFxEa0T+5uIXiaRbA4XtIoGzubN4K4no4PC4qd0xMbjj1SN5hKIY8MxduCDnF88tyfHZTVZ9VncNFLfOFGoRXO2T/yeBu6KD5+3o+DBare+kJuzq1alVGwDpPH/UyA+QtHjcZm2TagNkOS9c9+nXyzpIyPuFew7L41LL8aMgEp4vcg6iLd7oNXadd+z4fNav7MnzSrJjN5nOiVos66ACLdafs8rWociHOc/rrJ27w8jvdWnVJEBcU34RilqYFr+N0n95t4XnTXfSO5yNp3A6W7J4HgjWJUDJ5hSdie1Jp677hTUa/JbV4weAYFsJkG53yyKNzd5eD1dRAAQDQPJdxKKt9RCywf5lLkB5gz2abJIEQDBVC9uXFOol3e4WlZu7DmO/pL+PrBfF+dZI/gmAYF0BJOwGlok/pHAdWlcr/rYCtHovaroTxpTn7eTpGd+i6BwglWDIOhEVgHS/v28mC4SyK/6ma1HlgpEFULJVvtZBkns7pVaAqpygSjCIVgKg2022mleujdaiik5d1kC5AKEGgplYAwmrV6kGV9RAMOMBSjojsnvzFk/zWi8yd+EAEMxUgOJaKIZobJ/YcX9h2GPo2nsjSt/JUjwABNtagBhh73ViirftOIz+utqnR2dx83KPU7gnjx+QB/898f3HCBJYnv34Jfnrc/bTRV9+DwCCAaA+AqSzt98ngEy+edmnGdhGAySdl5zz1GdfANrkGdjV/NW/GdjGApTc2VWfl9wHgDADu18zsI0EKGdecu5s6T4AhBnY/ZqBbSRAOvOS+wRQ3gxs0wEq61MAVHOakJdfdw1Q1gxsAFTepwCoZufkP+3XHUBFM7ABUDmfAqAa0zrxLyX0CSDVGdgASOZT+QxsANTApkJRm3hXAOnMwAZAej4FQDWY6rzkLnrhyszABkDqPm005TZhMqnqvOSuANKdgQ2A9HwKgKquPArzkrsEKMs5SOGqzcAGQPVc2QvnJQOg/lhdM7ABUDNpUeH8454BdGsSQHXOwAZAHRkeqIMBIAAEA0AdA5QagofhgmabLBYAUAZAq3+nJv13bMzZToYV114ACAbbllUSIsBgAAgG68T+B1v+w+VAOPW3AAAAAElFTkSuQmCC)
Question 8.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQcAAAA4CAYAAADw8D1rAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAjISURBVHja7V0xb9tGFL4sXpKMQesgJ6CDi3S0TkGntBkMhXbdoUPTyITQIYaGICDQJICGoKC9eYh/QDw1U5whc4ZkbhHvBRIg2brZv8GuHsWjTzR55FFH3vH0hg9IREmm7r377nvv3uOR3d1dgkAgEGngICAQCCQHBAKB5IBAIJAcEDYi8L2Nfj+4N9rbu4LjoTZunh9sEEIuITkgnMLe3ujKXdY5uOUH93E8qiEMvFVK1w9H4/FVJAeEM8TgUfraC8JVHI/5CaJHe6+G4/H1hSUHG+QTQg+2GN1n/s4mjoVOBeG9NqUgjMZWID8JYV+GYbiMztBuPOrTJ7T/6AmOheZ54tHHpsbVmCN1OuTjRDWcITk4sMKFw+WJBD5EO9YTqq1Terj28Fl3ocKKLUZeIjmgakDIseOzTcK2XiI51PEjCbkky20UXefvyfuceC3rNddXtrYmIdtiP1BmXdJ913Ry0mlyCIPBSpeSo4mhTwEddvdA3HeH6z1K3/LrhHaP0vItMkz8HfD5IBisMuaHUbKIkONpaDTBDe99EA5WGCFf+GuLkJxLkmYtq2eQ2O+zjfbzGfmr6ftxlhxAilFCP0FBieAMJ+AE4Mj8/1wOC0Qy4xRwj6wfbPNVMrrnWOJFq+YN8l78TCQBCT3mfxdDCttVD3kX2W8Q/myz/UyEFrXLtnnIQZR4ecg1+mTSik47ndh0H8hhEAYr0aSOiSK1mpzwewLVAEpAJIvotYlymPl/tNrQk/5weM/lxFzWeEfkaZlCUgkLZuzn+7/Zaj8TCq22HzJdhdmXQRCuVCGH6bVY7kuQtWrxSZ7ntAkJpJj4XAnQE4ihRWUAIcWvD599K/2++HMuhg5Z9oyqITvswJbJJCiB08ivSsbo5yGGvfZL8g4NjnWN4QIYaCLPJINdV1gxlYb5MSO/niXT4ntPPpvKW5xBXiLrN0WqZHLdxax9nj1NOKwMQZ9t8/uDGD2tDOW/MbHfU3tDoGYTv7UwHOvMJv6aJoc8ZXDheobzTO/p4goCJDEt2rpYmxF9H9va9z0aupaIlNlTxdZGZDjpHpXxrQv2i/MP9pE03Udy0HEP8a4B9fwQyk95HAqrCzQFpROJM2FFTBrw/z7r/yn+lrQqEQuAxLDERNFK4+Rg8U5FWVVzwX5RWGKn/dpPDiUZezweXfV65A2QQx2GSEKHNOKJH1+PYlPIJQBxQOZdVA1JYnOyqsBnInLxb93nhMalnnj/YlIzL0chlca+twFhjC3hicyeVpPD5N74LlORVNdpP+UJqFBPUTb5q8uHanIm+knGcOcTU0AN2zQwSHGZdlLnICbUzhNtcXKT9t6mE26e5z8IgrXbyfuEnEM6Fhf2zpPfpRJiTMlpmtuwixyy7WkzOfie96DovqK8hEb7qfqmam9RGXKAXgxdPmSEHBDF+ZJWkMPvN39ZWvru88S5v7JpDIFkbc77wASu0lt05xr559qdncdN+ZA2yYPkgORgCzHA2IHvQj4BnkZlq61Vc27WkEMscZUz70U1Bgg5EacNa7r+X2bPKuRQpoel6nvOwwQO+VZ6C8nhbxk56PahwvgXyaHuySfUUdDukR94G9ywOvo3qlaZliIHhZxDXo+K+F2Mkg88Xo76YFIPOYGxEt5zmvWeNkGVHPJyDjPjMvGhwaP+TyV8qLCHpNGVBiGXf2J/B39tnv6NeapMdZODrEcl6oMRksGQrEvXoeT0yhyrFDq5SA58HEQfioli1ocq9JAgORhCMulTuzR8C1acsCb7N3SQQ9KjIhQX8R4VcTtRVDNiMVper4zP6HNCPaMVmvMos3nJobIPlewhadSZygykyyiTNCp6ven6fx3kIK5cvEclHR/nqRr4u7oXnHltl5/jUFNm85JDRR86Llvk1Wh2u8xAuowsds+RiZmZ5ir9G3pyDvPXOaTyBWf82RkKdTFnGslhLtvZElYk45Iq9y7hQ6dlekgaJQeEXPoVsr5i/4a+nIO+IiihRyWqThUTsEXqBeSzS0/Y0kQOFya63If852V7SJS3mUplpQk9QnIoHqdo1yHnmRLpeNFU/4bMniphRV6Pitjnku6DgfdEYUUSL2f3yrQ1vzV3WMHHBXxI2LURfOhpEr5NfeiVSg9J8o+iugZ+vegkIySH8uBjCisiGJefFhXH4Gek570JdoKvTdb/6yKHpEclnthxjwrUSCwL5fSpXpjziZP7npbuVlTpLcrarUjKpQUf8nqdF6IPjcLRchUfSjvqaQE5SOsewOi2PQDEdsDKl9Tzwx50sHa7Qzofb3n+H+D0uvs3VBN3MnsqkUPcoyLux4uEA9uXYg1Dus+Fv0fWK9OykFK5tyivzqHIh6r2kGiXyWw43E5LSER7wx6ZPW3trXAVZcuntS0Our5IiIWtLllFKNhzGpfm2hPJAcmhvj+O52S2W104RA5tOG9kIcgBz8lEcrAJkBxNEniEnvDEKZJDwz8Qz8lEcrAJGclBa3dBFiasUN3jte1Jx4j2kwPv6xC35+Omr2MbHxQM5EA3wwdIDhrJAc/KrIkcgu9/vLx082NbyQG29LxB+EOOmkBycJkc8KzMBsiB0P82w/Abl37XtKbHrpAXVA67TP5FctBADnhWZjMO62LBG9jYtsOJnDnxShc5iBJ9PB5e58eQ41mZNk2kZs9SaCLUoIR9sM2GzpyVqYMccjoKz8qUneJZmc1KcFeOADRx5FxZOHfKtqmwAs/KbHhFY1v7LvwWmzs8TZxm7iQ54FmZmHdwSQGZ2sZ3kxzwrEycWKqKoR9sz+a4RldtIT0TIYUxcqjSy15lt6KNZ2W2MrRocYFa8kyNLBiYkFnKbJ3SQxN5EDMsWKGXvYoDtu2szNarh5blHoSzSXMfbrvIqmxhEmeIJkJFuo9HEmhUZNH25fqhqR4PNALCCQnsIjHwZz6augc0BEI7QYCCKHrWKMJexYDkgKgVkO+BE67xcYHq42ZL6T0aBIFAIDkgEAgkBwQCMSf+BxvX1yIJiAlwAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJAAAABkCAYAAABpRbm3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWiSURBVHja7Z2/b9RIFMfnaqADCaLMVhcKuuxsSlAKtLEiWhAbnyuiFIgbiaPYgsJJlyZ/AOno7k6iveJIj5S/AKSkpFr+hsvt2B57srHN2rEz8+wv0rfAyUqO/dk3b96Peezg4IBBUF3hIUBuADT/90uR8KCbfaadAygMgweCsfP5H/ffVfGZJ8N1AFFNb8b8Xf7zZBd8/OZd5wAasuHnIAwf4OW3q31fPANAEAACQAAIAAEgAASAABAEgNwHKC+OQjFWBYAsKJTeOmdspmIokVa9ExlO1pLYVXRN+PvPABAAKtTh4d5tb5WdmLColxEFOn25DQsEgJa6z9jq8B/jIHgx4qM/qfltAMiN5eyHgohiigUAOaAdwY9cyykBIEoWSOwc+R4PKTnPAMgRH0j7PZlTTWspA0A2d2Gc/2XCkvlD4vz56/cPARAAKvF72EezPsmIDaW1NhSWMwBkyBciRPoDANUCKLYAw1MABIAqA5Q5sOI8mE5XFnNRVXJUfau57j1AZkohUeqXqJ8lMZqs/ne+5d47PLytP+t7G2+V5ZqEci39XT487UvdtfLlXPLVrC1hsVM7t0DGZ/S1iQzX1P+TwvI04Jc4whdq673h+W8VWOlOSux8BEA9Bii1TKveibY4eXAs8zkA1FMLpDWd7t2JlyoVo5lbnGsCVNazRq2XDQCVAJT5QHymligpnz5uwgIV9FeVCgBhCcMS1ieANCzmFhUAAaCfABQnMn3Pe5UuVwqE6fSOsaWPfCDpe9sTKdcXE6BZkVi+PwWAOgpQmosyYjhyLHZ1fkrFf1TdcgLMTATBbhI/Mnru/e05PGfZNXHWdYgAEASAqANE+egZAGRZ0t94mcaX5r6UmSoBQACoVHEbj86/xbk23SdGBSIAZEm6InHDly8za+Rta2tEpTYaAFmS2vV5k/BJkVUCQAColuKMP50YEgBy8IVQ6g8DQI4ta9TKagGQY041tUrGmwCoSmlLQwBtPrrL7n7fDMNHVF6ESptQ60pV2rzHvtzb3P+jrS9VFCfj7Fsa6uD8m9q5TqfBihB+CAuUOM4U++LbtEChnKwNOTuNyoWNUMe+lPe90eBDUbysdwBFlmcsd00TrSogtwbimML9LwtQlXdiHntTtKRH1RN9B0gX6eeq5aL8po7YawOgxeaFQsgGW8elANWtFaYAUMnogNbbmps8Yq9pgJaxPlp5ncSXTdQStcJ5lKKcY8ldXwNH7DUOkHHARJ331+s4UBNb3CodHcm3/ew6R+yVAXTZrwtWoneSdP4W3VuWYCYAUJ32GpvKdSRrWumr3/h65xIVAVRwbxdXri34eo0C1LYPVKe9xqba20nVP2LPpg9UChB8oJvRdY/Ya2MXplvG6wANH+gm4Sk4Yu/p6/dDq3EgY1ktupf4YAvvVeEujDJAFGqbde7NfEF1jthrAyDtC8WhhjgSrVqrtNsi5WR9xPk/eUscaYBUReGWGBxTqOdp6oi9KgAJJv6t8lxU2kL5Z5fvi8/K6sbJAqQCg4MB+3qdHQRFoZyjlW82AAJAAAgAASAABIAAEAACQOQAslfS2jeA2ixphQWCBQJAAAgAASAARAMgVQzvjdgnBVCVhCQAAkC6EKq0WAoAASAIAEEACAABIAAEgAAQBIAgAASAABBNgLoy8wsA2QOoEzO/ABCWMADULED0jrijqt9+ZX/fEr8fASAIAAEgAASAAFB/neiub9nzFPWwO3TCLFmAqM/9AkAWAerC3C8AZAmgrsz9AkCWAOrK3C8A5IATbYra3C8A5BhA1OZ+ASCHAKI49wsAOQIQ1blfAMgRgKjO/QJADgBEee4XALIMEPW5XwDIIkA2534BIOIA2Zz7BYDaBmhhtFDfMuWNv5ycZ9lZgOI5WHlWIT6ZHUA0Z2k7BxDUYyuJhwABIMia/gdM99OIZD7uyAAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
Question 9.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKAAAAA4CAYAAAB6+vMDAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAW2SURBVHja7Z2/b9tGFMevc5Mti42cpiZDNuvksUUGgyaMdEwbmdEUQ4ORHlAkAAejYLx58T/gqdnaAlnTIfkH7L8gBeIxk/03SOU78ugTTcrH44k8kW94i3yWyC8/fD+PEjk+PiZoaG0ZioCGAKIhgO4fKCHflRleSLuaIoA5i6LJBiPkMhZndtvolc+jLQSqmr326JtiPcmMeq/fIIA5AIdk+GkSRRsIz2rtXcCeIYAIIAJoM89AABHAxgHkgb+3ywZnhLDLuuAggAhg5QR3MCBfYu83RwARwNZC8D4j7xFABBAB7LgV9fFM+3oIIAJYTRvub1FCrpJ0J7aH/mcejR8xQr6mr81Y8O4ZAogArsxOTqb3fEo+AXBsHP0sQRJN+oDvoQesCE4+dPQNQJPwmU6LYq9Hr70g+HVER3+Z6NV7ACGkDCm5gP8b8+hR3wAU3uwh+ZyMxWLtwnCzYji+BghNx5O9BzD5n8UZb58A5B47kOcttIhzuunJyT19/egphGJTiHoNoAgjg92zvOB9zQETjza80NYP1rP908CnkZoPIoAI4MqLL1gr876bME6vdw6PhqsC0MaYdWXiheH0vj8iHwBAXRHK7ngTALuwTxD0YB4/0KuC6d+qzkeHO8MkH2SXzw+PHtsGEEatkKvX9ZYrES5pAeT2mbH993oA0v/yCXQVAG3OoNu2wPdf6eR/ASN/qnmz0hvM9NftBeoAqOwlnDsJYL2cxxxA2zPoNg3OpUoD2abz0IFKVtwIoKXq2zX44MJCGhGGk03P478ggI0BSK7zd75LAOo0iHUayWVrbsJpO48cLANQPeY8gKbz6NIPaOOBFdcBFMchmuRkNmC7Z5yPtxgLoluFAyXnEiBYNw3D++qao8Pnj+X7lK1py0C7otC/cMx0eBFwf08CWGcenbtoxQ+pNPXAiusAiouTVqVQeYrPUYor4T3o6F85wYGCSFSiSjNZrIE0I53RZtOLig3nJgHMe7uIx3AlN1lWhJjOo3sZgk08vXwyT23uitdSD6i2QtT3SY4lGY3J/px6Eycg01NCfSf6nHkAs55irouRdjoWqmCTebT13EjX2gLQ1NMrM9o5hEzorS1smMjmsMXvB+dUdn5Naa6TQuUBLCs27npddx5tLQfUuaiqrWMVrIQe0QODXEg2f8uOvchrWARwZkP3ZQCWHfOyKliZR7/VBtCdHND9NgyAmDS70x0r8efotCUy76DRlHclBBeF2js9YIV5tFs5oACNXrgIIIRgj3l/qIWC6h3UEE39IIKqVkYNWCdCcJYj3V4Du2DaaDzfGYLlMUORpFTqCoBvZWS8NY8WRcnyeXTnADSZQesCKAqI+O6W4PBg+0X8OV/lcSkjyPmiaaxxuArORm+x54ZzB40hAqQ575yM/A/TaLqRn0ff5IPl82hn4IMLChd5d8DOTDcjmM6gtQH0g1ec7/yY5YGUnedvFmi9qH1ASkcfZVtGXZOODLM+YH6Na31A8NDZfBn6fLEOAzL4su0Hv8ONYzqPdsbziRbHZHKQD3PJ358+eUAefHsaRU9czZ26Yi9/IP98z347bczxuHDSSr5QOHZCABHAWj2q+h4SAWxK904ACMl5lqDGVZBM3BHA1ZoN3dceQNmayBUDtao8BFBb91ld3dcaQDkP3Q74C7Xik3elaZ8LATTW/aqq7msNIJTe/jj6qcwrIoAr6iJY1L2TVXDSyDSfTCCAzeneSQChuVlnhowANqd75wCs+nA1AmhTd3ZeVfdOASiT47rPNCCAzeneKQBt7fDAr2drTvfOfDWHfLTQSjhBABvTvRMAijvQ4wfqWEhs4SnY6YIAuqX72gOY7h2bF5rh1igEsDnd1xrAZb8/VvW7ihHAdnTHn+pCAFs1BBABRACdBTAMN/H3gi1e/AItEcASANOnyfD3ghvIGxFAtP54YRQBDQFE6639D7OmBmBdbrKvAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 10.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:sin4x = sin2xsin2x
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQgAAAA7CAYAAACHbxRIAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAkKSURBVHja7Z09bxRHGMcnDQ3QgQLIc1UcETp7bKVK4gKdF0SKFHE4b04psFwgshIQ6QpE1u5cxB8grkIViJQ2RaCNIvgEIJkylf0ZcO7Z3bmd3Zvd29m32937R3qKnMzd7Owzv3leZ9j+/j6DQCAQnWASIBAIAAGBQFoIiPF/HyUJXhCk04uvBXo/1x933eFVwdj78aR8mBZ+YjnuChQJ0kVxLP5Ir/fsjPcfPAYgAkCsstWXQ9e9CqWBQPbZni3uABALAAjHtm73+87W7sHBhS49k2U7t7GQAQgAIqccHOxe2BS9o3XbuVvEN23q87mOtcK59WJ3NLqIBQ1AFP+BFGXvGiAIDhbnL4rETrYFP2RMvB847nId7yAvJNb42nO4hgBEIXOUdlJS9iRF6hogaHELe+9O0e8Yz9lxWYDwdnzGTouOK9GS6JALBUDUBIgHff6412NvKSK7KICgZ27Si51YNEvsFb2HsgHR1GcGIFrkYmwL9mwRAEHP0UST21O2sfVQFSDKcKkgAETnAWG6kxaNCWT59xNoDcVOHBC6opy8hTqk0ExsP8PiBiAAiIK7qPe8nL2hgpie2DxynMGKELYb+vWDZYrbcLb6Rs4Jfb9trT+kzwaus+zHKNgHxlffpP2mjId4C1gBRBCTOPHdv7EsWa8cd7AcFKydmVobqGUBIACItAViEKyj+RB9Z0cufG9+gt03qCo9jsdt/Dmkz/jpumU/pN+RgcekndtTMrF9ONnhY4teF5vw/46f5Klz8J6rAhcGgAAgWg+IrO6FLCsXA/fryGeKBZE0Z/HPJgt8vPvHwRSPh+gAEQUSP+0Ph1tFYihwMwAIAKLg7qnu2uRefHv/yac6f78oIAhY6niSAKG4G6cEiSKBRqQ8AQgAImHRb/bEUdbxU4xBcPZaNuXo4ghFAOEt1LFroQYcJ4AYWy56IHkxjUINQohDABAARInjl8FIXZ1IEUCQ9aDrDgwl2iErgWJb3C2SCkW6E4AAIJLiCr3NoyymNS2ivug/Vf9WZ/4XdTG08YGEGISMO4TuDz+9ef/Jar53zQ8BCAAis4xGuxetNfYnKXaS0rUeEAa+t1yEtGNToxOZ+469fldd+N6cyexCEMzULd7wHI3xvx2NrpkCQu746nsJ4xHiPcVHugaIthxAtBCACJQyaupqotx5ANGkU3eMAWHZ9xzn5heTOIQSg1DqEyZzxi3bDYChHKJj3w7SocFn4jht/uS7mLZSwkN5dL9t6m5UmeosetpSWQ1wdZz6VBcgsp5i1RofnpRYFhnRbirrCeY6/h+uf3Pu3Ge0QD9edNN44zL79/LG3qOyv5esLFkuTu9dWmAm32EL/kvRBrgyxtEEQNBGRc8S9Er5GwLn7+h4gtFoeC2edm8FIAgOskjIrywsFlQDINoBCI0lOqn+rDOlmjqOkiFRJSAoOO5vsvxEPa9kz3GuWGu9X3XP1HhAEBCG/eGWzp+vqjgnM7gAiMoAIeMkqiLTEQKyTLyuzYHGcYvz53WNI6urZuqeh3Gr5JoXW7DfWgeIROWhgJ9C2jIbkACI+QOCrEZr4H6ZsJtPLcyqGuBMxlGGDlYFiCAFnlrvosvKpQYuqj6SO38dgZ+/j/z/HBqQUEForthFxVf0MPPjKXUQ9K26AS51HMk6eGyig1UAIov1EFoR4mf1OyMDSziGOyJl+kemgKA0oB8s4u/iTUVlNiABEM0FBP2OqoPxBjjPTJ7RAOf9jWED3KxxhG4Re6mmqU11sBJAKCls0824NS6G8rInQaL4C1JJadqApFpJFM31xjUaXUuzngCI2YpdplXqK7p4HbEeamiAmzUOvZ6OddC2vzNtgksDRB4dVd2huQIiiyLEHyKPi0ERV9k/oHvgPA1ICdbT2axajqyAMJmbJkpexQ526lKsUl05t7pjV9kApwtapulW6G6YV6YmASJhLs+y1BuFWZjZhXWpgCiiLFkUQUrRGET4gvUQKNqAVLaLYTI3TZQmuBhOX+zoO1KnG+Dii7JMQCSNI0EHCX4/VeGq5bO+zYHVqhjENBWnAVFGAxJiEM2KQWQ5c4NAEeTyP5TZAGc6Dq0OKi7QPAChxl1MgdWKGITOcvEAEW93TmhAMu0RACCaAwhvx+47O1H/e/citdlTBqKuBri0cajfG+jg7xMd9Fyg7Dt3ZXUQGdweP7tj3dNmMZoKCBlTUH1MKlRZWlr6Z9ofjfqoeRuQAIhmAELm7rUy9rVTGuCOy2yAmzWOuA4WaYKrChASnhIS64MHAzln3rw5g5U1zv+Kb6aNB4SSvpw0LJFCOM7eFX2gsXgDEgAxf0AknG0ReZe5G+D8wGZaA9zEski5hXtKp8JAYn4dNAGEYOJvU/ecgvzUmxIdl7+mdHrcChejqYJKylCqatYCaOcr1X75jMyH627cuMQu/bfhujcAiHLmG4Bot3z/CfvjvPjxsNOACLvGZDupvoQVgChzzqu5gxOAACAqUVTy9aRP4weONClJAKIUqfoOTgACgChNvOBSLFWk674EIMqTqu/gBCAAiHIBEbMWJCCmD04FIAqPIeUOzroBwe+497DIAYhMLoYHiaCDzatAU9qzOwMI5/Ovzp+7/naegEi6gxOAACAaCYgoJNiZV9CU0OraekDMOU076w7OWmMguBcDgDARPzAZNNAklK+2HRCmN2tV4lrMuINzEUDZMUC86DwgpEvh32AdtGbz8ESfLinWvO6DMLmDs3pXCxWlpVqFXb4XQ9dlOallj5+nsEC3e5e+IA3v4KxaqXG7NwCRcUfVX7fnfa7pvmw7IOLnY9YFJZM7OKu3oppVHgxAtBAQuvqILgBinnGIacutfhcD8QcAwnxHpQxGcL6+bM/WlQF3Rbnm4WY0BRBwLwCIXJDI1ovRDUA04Tl0d3DWYT0hvQlAwDzNakXUHIuA5QRAABAtElnVuAiKjNQmAAFAwOROhIPpfQ8QAGLhASEhQZaEetlr9yyHW89hOQAQ9QEidjtQFfeA1i2Uuen3na0uLSR6JtNrDCEpi0+j8wBEDBDRw0JVqbfYBwKpFbYph+ECEBAIpB1WDiYBAoEAEBAIxFj+B/olD868KUdqAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAAAxCAYAAAAP1p+AAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAeBSURBVHja7V0xb9tGFL7u8e4YOm3ubp81tlMgE246NrVMaIrrITAIBCmgIWhpbx6aH1BPzdR26Jqh8dgO8S9oAPsXWL/BLh/JI0/UkTxSlHiUvwDfIEUS6e/ed/feu/d47Pz8nAEA0H2ABACAmAEAgJgBAOiWmIN/XxA6QURH7hNcAisVs+85O7ucXQeDes8Yn4qhd2wrAZ7rHOyL/iVj4nbs+09hFOASYlaEPHDc1ycXF08uLk6euA73A1E/CPfsuW1//OmQv+n32X90fzBAcAkxKyDxjofjF9n3nB67YuLova0kHAn2HgYILiFmA4GTmPnw9E02llZjK917MECIGbBIzOR2c3H0buY1Y3eROxag51x5/mhbMHYr31u1Sw4DBJcQcwEmk5MNzx0ccsY/O653oHW9FeGeueI5Y/wu+1kYIMQMtChm3x8/DVbamyibHa22qputfOaWst3D8fjFHt/7oy0DgAGCS4i5BGeet3kk+Lu8DGfsck9J0I7n78AAIWbA4pg5HWC9YKXYsys3DBBiBiwUcxwPz4lZJsfa3ouGAYJLiFn3g5qtpVDMPeeKCknUmFnGyWlCrB13u2kDfMzljKsQM8pFVyBmGQP3xf7ld6/efkmkU4lfr9f7VxVpKF7O/1TfS+NncUvfXRUBlHV39thfdN1nr97uLm7MFDaI25Hnby9qsF2qbV8Gl8vktyuTg2oHZffZ6IWVLaf7uC77jtxozzvbnJ+9o/8nQSt7z/cSq3C5I/c/vWaIBSvVYmO7WcTYoi09mtgoccinxKHq1diIZXCpgyv4L4vyq1uAbCs3Ji2RHcQlshGfnH8euN7hZDLeEsL1W4mZgcqieFBEkRTX2C7orkFX72ADfG+0HTUq8TsSb2Ibnrfp7PV/zbMHDKptxhWEH+oAUpgiV+llGBzlLnbZ7sfHmLCiiVNWIy5LzFX5Vesv8vJHrmC/QcwWxFhF3yWXzxn5X+et1tLgmqxtt1XMy+JY/bvDBOxYHOvE3BTHVfml7rOyrdpQ8P39y0IxZ4NtHR6ziMOBifu0KcnneaMdNXYh94j6eTnbvZZZetcZvKbXI9/bjvfUg9hn97pK1j4a4ChD3HRtu21iLuI4y6/0ZupwTJ8jnrITpRJH6zi+qcpxFX5NVuV0dRY/Z39Tk5QqRpvFHW2DOJIPWiAjCjmLkzxKCWtS7RZzGiaxZI93krWvkByi31F5b7K23TYxZzkOXcqAKx2/ictZkePQvY6bf3RiTkMe9jH8v5H/bV2OK4lZ2dGpMx6ddnVX6UXIWXNmBqf3MlnF7D5r9nUiRMOEVjTA6UqUuZ+bOrXtKkeUGQ2NbTLZatsDSziOxaPjWLePXYVjtb6hSMxzHLvu96Yc1+U3TX4+IjG34UWoq6G6j66/t2bErNuP18/k5sU2Odw9rGJbySwBGK2GeRwvKmYKWVThFol51uXmU5O989hTqMVvo2JeZLUz+W5drHpFz7tuumUQD5AmLmtSzN5QHJfFZovWtldxA1cxtsSx4OyTyrEqokXELMuH1esnYg68gTxbk3F4wPGPy+RX9QTqFN00ttqZfLcuGhbzwteViRjdLNqUmGkFKRNoE7XtFcW8srFVOL4v4rMKx3GmWLdqxoiKmAo5VkKAZeQkZA6gzsSBraYKLuBQDH9SjUPnojUh5nBFHnrHs7HXycZ+X1zK38mrba86o9uUADPheFE3O8+1zYuZA45/TzgOQ4BqHFfeZzZw66MMvvMyN5sNmMXMsrQyqjsfHKpGFNYmyyxzMIOnr9OBSbcfgu9NJlu6FXl2tVAQx1kyllYHu25tu21iTjieTDYUjm/o/rL8zuYyzDk2EXNTHNfhNy1m4dPB6HQkuQj58EY7e5x/0OVIINQqhua4Lz3v2VdJ3KzEzLr68lmQC+ceKE9guZdGWuIGztWrN1nbHhm++NsaMcccJ3FzzLHub+SO68cJsyKOC5NJsqY8y1eayFqM47r8Uukm1aHPXjPqdcjzNiBUAFgTgAQAgJhrXtDislA0vTc/ligFXkMxZ/ZoK9cnL//+7OxrtRHEVboXTGeJnf6g+5y2L3sy2QCHHRazFAolLGTwHmUp230qp4Stfa22CtnkLDHNwwrQl70OYg6ztJlB1B1b0xbirYApxFw+6ZmcJVbQl30HjtdBzJlVWBpB2wNb1tcKmHk16qRs2pcNdNjNDgUdt4+F5YrKGVRtoaivFTAcW8NxVPuywV1HxTwraPYQPq2zhTOltO51SV8rkL8iy7PEhqPTb8wmztm+bKCjYo7iJkp6xcmQlhMhVfpagXnuys4S00/m4hNW5TUQs3Sroyd0xOdP8fmm+1XeT5W+VkDj2ZScJTYTVxf0ZQMdErPueJqkoaCFJvjCvtZAzChwqJp3yD9LLPTIDPqygY6IOe/IkvD9FtztOn2tQLXJesYjQ5y8/mLW7T+3a5Bws0sNxvAssWRFLunLBjom5iSTTQOe9KlGD3e3RTwQs/k4Zs8S45z/k12VTfqygQ6KWRqCzbXZeX2tQArlgXuFZ4mZ9mUDHRUzAAAQMwAAEDMAPB78D5nr3T/yFxWgAAAAAElFTkSuQmCC)
Question 11.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:cos42x = (cos22)2
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAAxCAYAAACiV4cpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAXGSURBVHja7Vw9b9tGGL4sneItHWLktCUoslknjy08GDQRJGNay4SmGBqMgENSgIPR0t481D+gnuqpzdC1AZr8AfsXJIA9drJ/g1UeyaNO9B15/JB0kp7hGWzw4/jwfe593pd3IsfHxwQAgHYAEgAAggIACAoAIKjGNyDkAYgGIKiG8D33xQ7rnBHCrgdh+BhkAxBUTbx16PtOh3yJstMIggIgqJawx8g5BAVAUBAUAEBQAABBiYEQ8kAHvChg7kIxjE0rBBWGg8eMkOtogHf3QW9cP9zASwXmBd+l79SxSe6o8/a9lYLqku6nVbOGyMKLjSOPvYSgLMHJyfCh+4R8Tma6iKMgWEeQQlAQVF0b4bB9YWVjnp64n4cnJw8RqBAUBNUQoe9uUNK9RDcUgtIiCIZrbo/8zQW1fXDYbVNQy1ZzVHl+2559EerAaY1tZoLiN7rXEWF7500DalnXB/IMxRx/3yyTkVvmHb20wrZ6m7t8PMkSM3pL2d7pMAjW7Mv+0+Fs5pavzRm6yfpA2zOa57pvyuonqYkxskFQykmTvxuLasFpc7bQgqpaly1KfcYnCpOXHb+8NBvMW1BxoFL6YdPzd2X3EI3vxhbBS5zdrKCgtp4/Io/+2wrD5zYIyqQuMFnNUXYNLib+QvgxQTBYdxz/R90z9Gjvr8GA7auCQzWWadY23Ea5/fAHTdZSBu+sODXhrC2+jra+fffNd4NzraCKlv9Ms/C0SVCHB6+fdSm5FDamw3bO8nUBP6ZH6cfM6tDuZb7xEt83vQ6/hu/3NxjzwszmMfKH6YqQPUZPeUCoAjatEW4SK5xYLj/sP2WEXKX/u5tVxuAThOrdhH40Hkou2uBUXEfFqQlnbfJVKKgkUNXLK4qWWiyToBKLQL+6nv9CLmjlukD8T/AgBcuI9cNX8jhFo4FbpHjcBY2ZwjFFxX5RBkgsGPkkjyE5NhJp+iyzAH/GfHxMk9N4UlJwWsZZW3yVZqhlsXxyRuVWKhZUEKwXZVpRwMoBkQiBnhLqxoLMitxc4Z0FSTousTZRDob4f5rZtNS2pM9aZKnSe17xbpvjeT/J55na2yauJOGAXcj31HHqMfpbE07FmFJOf63DWV2+Vk5Qmkw7Kmvjm7RXs5ecO3fcTaK33LbJMyC3Jq8PDp/Vscv5hkWRoCaDMBlHaXfxnu2s50pEkyJ/z3lwWoWzsf0z42umNZTJubrr2GD5yoJVPkZlM1IhS159om4YqWqC0hk/si0yZ9kYpVlaVTvwY6ZhzXXgy6hUvM2a0zqcpXzxSePnVgXVtIYyOVeGbYLSzZTKYxTfWpJx3Z/peBC4vc7v2SJYw3EnBb6Su5GuiSECynNpmK8/ptmI0MWEzKluAmiT04JtFkrOmvK1MjVULUGN92SNqOuFvAslZjkxA+s+FObrAP63w5xf5AAxma1NGhRFNZSoA2S7VCUr1spMjr8/WbMO13Y67Eyqe66MOZUCWsup1B2skgFVNVTE158ZX7GdrMbXwguqyvrAul0+aUYbya1VIY7xMexa+Pgkm4xnv6wYT5fixAHkbe5G51w1+cBc3OWjH2RODg+2u6Ko5+OcTos8x5OAlOVb5TQK+qqc6rt8k3zJTRBTvhZaUFXXB05mHvavaSDzL/7pEqfsm0nfD5/mbYr8XYXS3j/yMfELc703vr/9fXYcZRdNdx4LDvKCGjcXkgCUvrVkXLX5LarAjirvVZPTj21wquKsLb6WwvIBgC2wWFCrvR8KWFBBzWstX9k3GAgKgKBMs4/Jxz0ICoCgymG6HwWCAiAo0xsa7OGBoAAIyqDRULSHB4ICIKgKKNrDA0EBEFTVG5Xs4VEKKrfFAr+qCtgCVVzORFBV9vDI56RrvvDb5oB1mOtvm1fdwwMAS5XJWs1Oiv0oYZ+9KtvDAwAQlCY7Vd3DAwAQVMUGBSwfAEFBUABgraDuICgAggIAAIICAAgKAJYA/wMIu1A+kI9SSwAAAABJRU5ErkJggg==)
⇒
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU0AAAA4CAYAAAB5aKoCAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAqVSURBVHja7Z2/c9RGFMdFHegogPFeFcgMHbemDEPBHOJHSghn5ZrguPA4mgkwc4Unkelc2OnjNCENUNDCTKBMCvwXwAyUaXL+G+xoJa1utbcrrXT6dbpv8W3MoZXevv3o7dvdJ+vp06cWBEEQZCYYAYIgCNCEIAgCNCHTTrWsUzrBPlAXfRvQhArL80bnqWV99h3peFZkYrveFdgJWkS5Nnmk9mvrmAy2ngCaUGFo9q3+25HnnYc9oGXQjkPv+tB8DGhCgCYEAZpQW6HZZN4TuVbYD9CEFgqanmtfocR6H+U9j+hg64c67tV17Ns3ae/AsuhnRMawH6AJLQQ0GTCv2s5PG7u7p3d3N047NvF8eJ5QZ+dulfe5NSCPez3rA2sL0CwATJs8gv0ATahmaDJIjgaj+/Lf7BXrnUXXntVxv2vUegZown6AJrRQ03MVNOtyQgx62A/QhBYammy6TujaPgY9oAloApqAZorG440zrnP1AbHIx8Fw6w4GPaAJaOaEJo7dtV+qPiq0eh6eIvoUna44YcL0HNAENHNAk03R+sQ6ZJ0xdL2LTRuFrbTWaZSFiCg1fTTP9HzHdc+tUbJf54osBj3s1wlohh3RjrPK/Cw1oGnWR2WcCAqvTY7q6HsMethv4aEZQKp384Dt22uDQRxKvVu3yB6gadZHZUCTOSGgCWgCmgsITTYFtYfetTZMz9uU3y0TmqrnCqC5Yr+rwwcw6Euy33h8AdCsZywrQUWs/mHTTsz2Cw7o4Gc2cE2gWeXZ6a3h4A7LH7Yl2k3rozzQDK9jHfXozYN7m9uXmO3Y0TxCyN91RJlsxd5etV6xQX9jc7vftoXHttcibbv96go88kCT+Tcfy0XvRzOQyMfGc5lD+xp3hCxohltlrKNwAYMcsX2GG+PxmVKA6bfNV5XbBU11H+U9EWQT661Yb5PZznV3ztURHczURazpFJKJtjfvXQoX2qJ7I/1D5o9tiq7abD/NC3pCh943TUFTqMfJxvKTTkFzdjDrt8FEznMiOdBJmdNLHpF1DZpdTV+U1t+243EfYi9m9kKuApxd39oXH81lNQ0ahKYI785BUxXtqYwSwpW8vOq4D8Twm0edZRWdADQz7qdjNTyD2YX00q3qeOky1D8NoOaDquPQtI6ygGOS6zHJCZnki3TQ5AtFuuiTP4PqPkzvi0mGZpHrVREJqfqo69Csw+/ClEwyquTQnMen2gLNOscue75Vsvp8NKLrbBYoQ7MMO2ZBUzGWY2gWYkMRaMr5HraQIOcQ2W9WCXmTlhMKHCa6DruG6w6vUOp4pUQK0YosNxKf4rMIwvWGF6Pv6ATTevlZE8/n37fjhtEr65iU633SXS/LIfN+KGpZoem5vp3jup/z+R2/jsrvpn1MjtiR0jivHp3JL8MHmuovExuy3/g2fJ3Hhpub9/qqscsOSzBb8BysCM2y7OhQ6w/d7xLP6z/HcGtwh0NT1f7m9r1LifYVkXFuaIahtj81dNzb4u/F6YwcmbEbjyCUmDKz7RJ04K7zN3mwfaKEZDa7jvjmSeRUovajvYgT/hy6qbh47/xvea6n6mDdx6GkD0U9BjSTftezeh8kv5tk+V00YBLTQtnvgj6R/E4cUCsrK//I5/GFvHt8bVMfaKq/cthwUoYNA1ZQZ0+Y/c1ASLYje0HltaMOmuKzhFHm9Fl4pJnWvq4GQ64BqcrrhLAj+xaxg46PgSLlhGK48ggwOumTePOwv80Zaeq240zPV/vRw2h0358yvJB/o6slyaf74nMnruc436qu1+XpuRgVj8ejC0Gb4/GFKtIUOr9zKNmbx+/4PUZ+94vcbrj4IywsyhHZrA88N7F7nbYr0YYTvh+UP3eaDeNpeWQPHTTnsWMaNGMY+mNZtCe/DzGnqWw/Zd9rvgFpMHWPnVQCzzQ6C0+aiNGauE9wbscg5KVuEWs6gNSnXXQLPll/r+v0TJnQNEkR6AawJlo+MdkCU6TN0v0uiizS/I5Px2OwRNM7eTCJU3mTlfU6bFeJDQObhc8o2fB3lQ2Z/cS20qBZxI5Z0JSjzKyFoDzt51qZlRdYdFOAwAkUnR6dl47/v5RfOZl3L5w7oOtZORBekCJt+5KmA5Sr52nXqzanOd/quUmKgKvMKWaRNuN+SVl5LdPvVMdI4z1+yusHPlDo29tV2E7QqaI2lH0wjw15TVbRn0Vo6vxbtGOeAEoFTR2k01bP+csxq/18A1LzJlL+RrFPUlcIgnVA+IEo1gHFjtSZnBrinan7Do5qGp4ZaYrXM9hOUV5Oc3m2HIl+p3Pmon5nr/Z+k/1Od7Qz+Ltq6kqdvTw+0MwiWhRJZdtwokpFGNvQj8SFTeSaiHq2EJBkx+M8dkyDpi6iVP5dat989TzoRHKoG5B81TnY+Osblr9JeJSnWiRJTJMipxOPSeaJZLUR5sBdT+aKNs7c7NED7oxRjuVFIncjheLx82nyYmKob3K9aiGl76POQXNa7/NkxV7b0fqdtDCT6ncCFGS/C19ss+e55f2bYt5OnsK2Dpr12PA4bQE5Lac5jx2V03P+vNILQAXNuH2/v03azzUgxYePl+mF5XruTNPf0M883xHtfYvfMHFiOjryGJ57Zol3+imPA0XHHE+UiiJinusUjbC9eaPPFwjYPc5cz/+/7L4C+PpRcHxMc9V+5e6450yvB2iWt/Jbmt/5gyLN7+SIKz6Tz44BRoNT5VPiopOpD9S9el6XDU2hmWLHiakddavnccTbX/uTj2UWFYtjecPbOJ/e/virVGjyJXgxQlNGdr4DRZ8Pjfd6ycWKk9/S9sNksvpa/E1gLNt56Lo3vp7uo6Lv8yyoCOfCleKGlGtPCttJZn7LI9f434n9lt0j26rBP3Wb93plKquPmoImtehfVbdZ0O/eFPE7+TosZyf+Zppmmc8H6rJdBTb8PmnD/mHa2NVFomXYMYCmZjrv2lcfxtdj+0ClsSy2z8AZtf9fon15Q748NaWj0bo8bYbaIZM+8rzrl89aZ/+97nmXYTNoGfTdl9bLL+iP+3Wd4ZfC5GAu33i1dkgtkz4CNCFAsyZoQl2JRvNDs6m6kW2vV7kIgv0ATahmaDZVN7Lt9SoXQTN1ZPtrv5ZVRxbQBDQBTdVvU+pGVpmiaardLklZhFhz3BPQBDShkqBZZ93INrTbFTFb3SLkhaKO7KTMOrKAJqAJaKrglVE3sjJoNtBuZ/o4vY7sMaAJaELVTs+1dSMrnp7X3m7XFdWR/bRsX/YENKHaoJkEWFg3Mk8tyHLAWW+7XZZcRxbQBDShCqDJlFU3sio11W5Xp+zEou+X8fvxgCZUKzTFupG8zF1QN7LiwWdarxLKFl8YWtadB4AmNCc0zc+eq+pGigVLqrrHptrtqkzqyHZZeb5GCWhCc0EzT93IMtVUu12USR1ZQBPQhMqGZkbdyMqgWXO7nYwwM+rIApqAJlQiNE3qRlZyjw2127UIM6uOLKAJaEIlQ5MDLFk3Ml9N03nA2US7nYgw9Z+TOF7Gze2AJlQrNCEI0AQ0AU1AEwI0AU0oJzTH4wt5Pw0MQW2XyqcBTWhuaEZfHVTku1CVH1pcpeVyAU0IgqC2RrswAgRBEKAJQRBUif4Hya5JZ0H/SsAAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
Question 12.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAAxCAYAAABNuS5SAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOASURBVGje7ZixUttAEIYvPTwADOvO9GhNmVSMuDCkJIl84wpw4fHcTIAZFUwQdC4gPVShSvIM8ALwDPgJ8DOY3Ek6WxGSLNmWCXiLnWFuLM76vPvvv8vOzs4YxfhBEAggASSABJCCABJAAviKITD2LhrxMwKYEZ7ka8DYowL15AfwG+k5VWTsITzrozjdJoAZ0ek0FziwGw0MHe+TPjsVuM0YPHIhtygD82Si11gKsg56thBfalD71fC8pbnUwLz6lVLOPQ2RS29tLptIpBz7jGG34brLRZ6vI1zoZ8FuH80lQGnjnskegewnW+G3zU5nIc+zx60NC1CcCw4nUT18dQDHKb/0krTu82iZ6zaWje4Nsxh6G61ja+YAk3xV8TLCriO96qSNwWLWzSiArttc5AB/orD8bPT1ELs7rePVmQFsO+tOcLH2UNADq/6j6bqLRf6HQDhXX/xhYoAqA9GWe6PvU6Xua6ayLar8I96wbyLNC04VXuCdhpeG8VREh6ZZBYLz3bLvnWr3+wjwe13IrwNBF3zLuPwsN18GvLYNh7O4c6ojEXe8DylZ+Qxg0uyZ1UTyzqkhvCNtQ/TfujnYtvxcOsC48GdFIU1UmaD1LCrk+qWUQt/rEq/U+GWrtWMhCi8Q753VTaxcRbunFnmH44E+czxZDTRSyQNY9/EuOdQzE4GulQ7w+cXJAVweFOuo7Fplw2H8zIi7Ln3/bqxfD8cp3YCUCQ4Bht/Nb0rrXHzTujaYGtRzb3adFVgBvItmXwipq02qyWb/DMVJFHAUYNKZ79VW2O1LNKiZAAzMKPyJl09081HBzSvtseKy8CoBTlMD9Wf0SJXWBT3pVBHY3cDmxLRsVgCLvHNq0ypDA3XjiH8u3mUNSF6rXA4G/xDODAH2i0apJRxYCNxHu70f/dV0F92s4JWZM220v0enk7jVmUsNNP5rsBqPR9gtzYsD1i80RP85Nf4Zq+PPpRpMuA0xP0BwNhzutRXSzWicldV/CVByOMhKfZNdPkAudqXceD/QQcC7tBkUuDgZ7veMrxNbod0Jz/71mW/GxsxDEAQC+LK7TII24S6TwE24yyR4E+4yCeAYu0wCmFcTE3aZBLBAJO0yCWDOSNplEsACTSVpl0kAcxrprF0mAczROLJ2mQQwI/NG7TIJYCa80btMApgSeXeZBLCM7CUIBPBF4y8YNiDyyDH/ZwAAAABJRU5ErkJggg==)
= 1- cosx
⇒ ![](data:image/png;base64,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)
= x – sinx + C
Question 13.Find the integrals of the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIAAAAAxCAYAAAASqKEbAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAASsSURBVHja7Vu7ThwxFDU99CHC20EPZsukQotBUCIxjKh4FCs0EiESBUoGOqSQD4AqlPmBpIAfgC9IJPiC5Rsgvp714B3sGe/urHezc4sjJfOy7/G5D3u55OzsjCCqCyQBBYAkoAAQKICRmRAhEzoqvTgeuBgpgw+CekAJeRLGvhBCnyjb+r5/fDxVxcX3xcXIGHwasjVh7HMGL2SG3+6fn09WafF9cjESBp+f709ySn/Ww2hTXYtCvio8oAWGs/B0rSqL3y8XtpRhSyF95SCXHOWSw+KIz/Mg/mjxBKPRNiMHliu7tLVXPnrhAnB8vD8V8vphWyjPerQ4aS4tQDox8mgz+KS5MSfeulchqMaWr/QcBPcXKf2dhii6cL/UPFnonNT2e/WN2iK/jKJgnrEwds6DDXpECHvcjuNp/XqzubEgx2Zb16mXNNiuNJ7ym7LDZBEXPviwcdHxXWF7EMWzEEVCRn7QxsGRjCgz5NbGizUHUUL/8jBaVaqUBUlbVUpRMEByP5hllNxJhQbxuvrOFiPXrBHtqtAGk9IXrQjwvhrDnB/pE5AcMhaD4YPKx3lc6B42SD5MXCjPlwucqQ/kPEXhmAiHtngUzzulAKUYfbBksvRCKiyOZq0Dyqo1UWkcb08zQh6BABXu5DVHxSffY3cmxSd5sb4pxxOeZjPOFppt6JYLmFvqYb3z8bUfLkAYptQA34aIpAvTSQBq4rZckxqWUW5KhPBKWJCkmCE3MDkImRvNkznX/KwKobyFtRFvgvS0t1X1G2SJKuLCBx95XJiikS4AEFwRP6TbYkPdN4WurBq1UJhsYwx50ejdIp+7VP55ebHE7Vhu5T1oPvK4SOwnLyYPjwO27rRrcFW0i+oSgxPFd74TzPLF2mVieP6CgVFZg0yeAgrnjH0r8tB+UMTFoPko4sL2fVWTuNQXxESsCB0PoJ4ZvnUK1a7KkaBG2J8moa2zwMlWm/D/Bmt80avlIo86aLA91jjY0/MyFDnLNXalSFIEhJzvRKfROzlmF4VlVwIo4ALs0EN7mXy4cJEIoFNAaVHoeH5SdBL10oG2Ma/32aPKZdlqMy2g2keYkjRRuIl3HkyKF+9/fjOeQnuB5Rji33AwosaRJAjv63aL2cOpnJGLzmfK4UOF9jwutOegdgHuJtLtKmV3Kyv0AqKHGsd0tpB7DgAk12rkT7r3FftWfasFoU/LZ8+ULv7S70uDebgTRUsf0ufExEzFjDLEBqVkRap+SpZs00iLsvBiUEfGRVyUyUfE6ScXLjp2JK/b4ladh4fAQzs1tbJ8jexvAYgh/eKIJKAAECgABAoAgQJAoAAQVRaA669miP8XRQJ4Row3MAUgUAAIFAACBYBAASBQACgAJAEFgEABIEZ5kbrs9/MuAF99c6Zni64NYhF82dhrv59XAQyjb64KvYH99Pt5E8Aw+uaq0BvYb7+fFwF46puz/pn3OPcG9tvv50UAw+6bG9fewDL6/bwIYBT65saxN7CMfj+vEWBYfXPj2htYRr+fHwG49s2V3Ec47r2BZfT7ed0F+Oybq0JvYBn9fl7PAXz2zVWhN7CMfj88CkagABAoAIQD/gEg9SYZ6lpyYAAAAABJRU5ErkJggg==)
Answer:Using the identity
, we have
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWEAAABhCAYAAAAHiBBjAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAABEHSURBVHja7V3NctxEF1WyJg8ApGfnsGZ6vIRVaqwE+HaueKzKhpAsXC5VOVDlhYtM2KUgYW+zgRXwAlCFYU/yBKTsvIA9r+DxNy2ppVZPt9Stn5FGOouz0Yx7Wsfqo/vTt6/z3XffOQAAAEAzAAkAAAAQYQAAAIgwAAAAABEGgIYWg+PcEIH5ge9VzA+LDwAW2J9sTojjzBaL7dpxyIwMd398cnh4C/Pr5/343ubOYn6Xq5gfFiDQezz36OeLxTaXcO3cdv+ubeFZWFZNzK8hvv9pw/1E87tant+4lvlhEQK9xosXT967R8hvm56/k1hB7n1uBVHv+edV/+Z0+vD9oTM8fTidvl9kfgeee6/O+a2a79T9TKZftHR+F3XNDwsR6DWmvvuxO5l+qrGGUiKnihEWiRnaiHDO/OYqEdbNcQ34ntfBd6XzU4hwWb6xEAFAgf0x+dpx6DkXSrY4kxhhGArwp5MN6jjn0bW5qVVqI8Km84uvh7FWNs/5gG6dMPc5/C6Zuf7049bzfXj4gcD3RRV81zG/xGuKY8cy35d3946GEGEAKIhd6vxCxvtfy66qS5xT7pYyaye0kMil6/n367CEbebHrTVCd19FAvGAfYd9dyEg78r8Xsv4vrDhuwp41PmZzU+0cEW+2fUlviXBhggDgCGO9u4OiUNfq0SLCWhojZHZ2PMejMjo1zxxk93qw8OHHwQivFikRbZBhVZien6BYN12/pYtXo+Sl4Q4b4Mk3osX77U1JJTD91kZvrNgNT9BVJMXBJmJFm+Kb8MkHhYdAEjWF0vMZLnuSWgivQCzrCjlbgD5GvV+Ljq/SKzeyRYvj23LVmYP+L5ScJ6CbNkW4Ptctnhj69hgbIgwACgsKH9MvzKJNe5S8ipabN/YJomKhiOy5hcLlWTxZiXw1olvZmEW5buO+aX4FizerAQeRBgAcsASKsT1n8oLUbkAqffSc8kz2wVXRoSz5qezzNqclCvD9yqE2HfJUzY/8bcM+TZOykGEASBaWPtj+piO9x+nY7dPbm0N6Ikoliyey+OSurhg1SJsMj/VXJI4sXmSaKUWZng/NwvyTZuYnzsYHTMutXwH15Z3UUCEgU4KZxXWUChw5Jt4K5QMuvtLIgiLRUjI76Lghkk8Vn5L323vHd2pWoSj+X1tMr/nD+lngst+M/q7OXXpD8x6ZHNV7YFtgO/M++G/k8H3Zcj34UdVW8TC/OZ584v4vpL4vrLlGwsaaExAyyzsMCZL30386UZZlzMreSPGA5MEG7lk7r2wl1X5/SwRpg79y0SEo/ldmcwv/P7mI75v1SH0NdvKFfwecV47xD0tukOC8236oqnifpIEWzm+65qfwPeFgu9/HbJ1arJDAqIArDYOWNHBLWGihp6XFWEAfDdulIAEYFXIPIimpXtYAQAiDHQCTRyUAwAQYQCIYHNQTvBgKg5FUX2uu9alw89XIgTgGyIM9BOqg2jYtqQgkcQORRm5x3t720NKvSn//Ghv+84WHZwQZ/iG/x3LpE9c+pRd2z7au8M39ztk+MZm+1gfkeKbbp1k8h1tvWJ8e+7mAfiGCANrDtXBLewaHftf8TBGkCWPtmIlm+RZPDkp0RV2Lsw2Xe+AxZjjqiZhGxeg/h/k8H0W8x2JcB7fsIghwkADbqztYSmqg3L4GQhiVVRwjXrPZOGQz0mQr8XFCkj86cNE0UvNmG+hCEG+FhcrrGnHD4gwsJbQHE6jPCxF/DvdwSji8YUL1/gnti9VJeBViLDNC6RrKMx3CRHuO9cQYaBV1nPWwS1Tf7LBY5TBFjZFnLEiEb4yeYF0FDcK8V1OhPvK9421EOGutfMGD3rkHdwSu8ULcXBHg2M5/otwRPXPnJLvDMFFOKJj4YiutfMGD/rFbnIQzZiOv1UcD5jaxpYpChBhY2TwPTfmWxRhzjdEeH1EGFVU/eDB9KAcbk2xljFsIUdtY3bEbWzBwS7B6WBJ25vkWnKqVbD1ih903qJTxNomwlXwzTuGcL63Dw8/BL9rIMKoouoPD6YH5QSi4Hpf+v7dT+I4JTsYJUrgCQ03k6Sf602j5NI8OWDHu59sZQvc6/M291hrVITz+b4w5PssxTdefOVFOC8+aRK/zKrEMa2iaqL1dZn7tOXCtppMNxb2ZgJAh0SYVckIGdO4nbP4+YiQP+M3nyKjGjQ0JM4bXeWTDmIV1VKrceKerrL1dR4PNlxkVYHl8ZC6vqZtzQHzFzbQH66VF6cT+gVxyFveVjoSwhmPT/KDrHmGW9jici22esmqxMmCXEUlt75OrES7VuO2yOMhFOD6uFBVk7E5BY0bk7bmO+vS1hxAEnqlITC2NmIDrr1cq2NEt52/ZREMasMXVuhk6m+oMs6xQEVCYFr5tGx5qtuNF2k1rnoTmm6qzuMhbrdSExcqHnRtzdmB221vaw7kJF8hxHVwfaXg+p+2cb1s/UUCot9IHwmMZMXJAiFV4pzoKnGWxiDkd51LnYibudttXNEl7VvN46EEFz/lcdG1tuaAOvl64Ln3cJRnA1xbNmZduQhnJYPEz1WudOgSJ39rUokjWqwm7a/FVuMreJNmLo46uDBosz3TtDXHQm4xcpKvrWxJ31mu2y7ConWnbT+tEIJEeBIr1aTyKY6VGbS/Dlz0pPV1rW+0PB7q4sKgrfmSJYyk3PpCl3wFauS6ZVvnloUlOSrw+ra7+5xv4OYWGjPx5SQZQ7x5O2omaFr5ZNpuvIpW41YinMMDuwdVwrAoF7ZtzbngptqaYyGvHVTJV6AesNAk47ptuySy3Ozlls+RqCSfh91XkzbRYVdUURzEShyWGRbf+qZVVFW1Gi8YktDykP5ODhdSVZLIhU3bdf57UZvtuD33yB19X7atObB6t1mVhAZq5LqFBSTaD1jF1mDg/Bfvjx25x2KnVXZT4v5ZQkZ/iJ9HlTiPdJU4wW8YVlFpWo1f1tn62pQHCy60VUk2bdfD79fT1hxYHXTJV6B/XOOfBACrXnSGSWigH1zjHwUAK4ZJEhqoyJNdeJmMa9VRqRBhAOihVWaShAYqtIBDrm+KXLuD0XGbuMY/rIcPZ1VtWQBbAQ6SqLnJV6Ayruc6rtv0fOOf1jMU7QkHlHeLs9r7ID7cX67xTwMAAGiLCPe5+2wfu7zWHc4AACB/XcoLrK+dZzuJOmLC4BUAqu2+DHcAMWHEhAEAMWEAAACIMAAAAAARBgAAgAgDAAAAEGEA6PkCReUiRBgAgGbAjicdOsNTnCkBEQYAwNJ6lfdbFymiKSrCut8G9/VyUJR3LBoAqNJ6TRoOXPN29v50ssFbZdmcXVBEhFnHFn7gP+tyzjq59KUHYcT9hYL7M1vubeF7mzsa3i/zWrBh4QBAxZB7DzJrKGxLRS5ZF5S6LOG49RXdfRUJwwNWdBM2ne1HD0KR+48n3/5P4P7ChnsbiLwHR2jKvOe0VKrVDbD5XGfOt8nFMJm37b3BjeyoVRY3iiWzsec94E1qbZ411tw2EOHFIs57xpKGr2mL16PkJSHOW1VH8I5zf5biPk8IC5bz65oOp3gXGvzWJsJHe9t3xB5r3BwXPx8R8mdcFkuGb2QTPXjgiPOG93Hb29seUupNl9w74p4Wde+qvi+be+PjiPcGN7IvoQmzruCakvLrpWvU+1kjPO9ki5d39e5bGbot95OQ+yuTcn5RiJOXbdrilRvy1irC0wn9gjjkLTf1o5uf8Tcv74rM27lM/YWAhoKUahPPTHc69r/ib5fggYwOula1li/i3lV5X6EAl783/lvBQkncyJ2+uZFdxS4lr0wXY5lwRCw6ksXLxaCP5xUza7Qo99ZiL1m8Me+CDtQiwnFbe+EtG4rM4uYXFutk6m8ELpL0YMSCFgkMf4vz+Fn8hqHesyrdOysXI+O+2O/G7l/Je9O5kWzx9s2N7KQ1Rr2XnkuemS7IwiKsscj66k3J3PP4cH1hJyXvlyZWeBVvgZnuLRsLktS6RRYe0dJlrvj23tEdFWGJwJk9VMYnhklNF/Puq8S9/STfG9xIc9QdI69yfBaC4oaCLm5YpQirfiN5FvOTQ01yX/XYMfeLe5Z4oVXPXct7cI2em/BeagJcKHRixT9X9c8KXe3kbwVXPoyDKWKrsntX12LMu68q700V5jCdw7qKaNFFF/7v6buJP92oL3RQfvygmSQhv4vPLw9dsfHZi7hqEQ6emYf0M8H9vsn7rFGX/sCscDYHdzL9tAw3pnNvauwM7i/D3zj8qOqXScT7lcT7lSnvlVjCusZ5OoFJhCqxaGNXfSFY7mhwHApW2joMyExcjGtb966q+6ry3nSWcNfcyCjxOAsTTWRGhrs/5mWN1TE+el6XCFc1fuKBkUv2/xP2r1r1OQufDfqXTU7Adzcf8QSvQ+hrltMIxmFGAHFPi4a26uS+yrG9OMEWhgKKcm+LiPcLBe//OmTrNOtZryge4lzfdnefsx/iVg5rN73p+TtyQi1+WzE3KXoomPk+puNvFYHt2BKswr2r6r7YnFTJwiL3Jt4LF9yUG9mBpBxPUixl/RHvBgCnygWWbisdiVDyeehuJO2oQytBFB22O4ALHrOcgpjKQoSqcu+qvK/0d3LubSGyunsTx+FZXO5GjtzR92XdyKbB7v8eIb+xF3JsNXjufb7tEF2GAYhwFab4YlENBs5/8X7akXssuhbMJRD32xIy+kP8PBAq13vk+3c/ib/HTPpIyDTu3WXtLkbOfVnc25e6e6vbjWwajB/VC0QV884raFHFkm0KeGzHb6I4qDEhaJD7smNDhAGgAEJrP/EG8gpaWFHMFh2cEGf4JvmbJ7cmLn3Krm0f7d3h+0KLFMzI49uMve5IcUO3TjK5ibL9jB/P3Tyw5l4Yn4lq2bEhwgBQECx5KW6/yypoEWP0Ypxc8JBmm653wLyF2EuSdq0Yjh8nTG3G7sL/Ioebs5ibSCjz+BGtVt34VYwNEQb6GcMqWASTWFYsnk9fczE1Kdbhi1lOVsrXVEU0Rcc3GXvdwV9AxtwI+17la3GSWageMxk/FN302PI11dgQYaC3MC6CURSa8ESdGBPPK2gpK8JFxy8iwjYvqCZRmHtLETYZvwoRXjfeIcJAYxY03+K3ZJEZFOsUFeGi4xcU4SuTF1QLcKMQN5YiLIz/r278ikR47XiHCAMrB0vGySXicrY8q1injAhrx1eJSo/CEdbcFBDhvPERjoA4ACtY5Ptj+piO9x+nz8t9cmtrQE/YQU95xTq5QpATjigyfh9EOIObuTH3olByfoRwRN74ZQQeIgwARgJMvlkqeuGgu7+oClrYcZ7pLWxRJaLQrSK5llROBtuheBm4tIBtxjcduwsiXAX3/BB6zs/24eGHueMvODQYmwpjn4tjQ4QBwAC+S55mxcji0u2MghZVcQ5xvWmU8JknhTze/WSrWeDynsdl7pbjp6EfuxMinM/NhSH3Zyl++ClmmvHLjg0RBgAAACDCANDlUE7XS3bBPUQYAFqJKo7+BIpBaF+/Eu5BOgC0DJlHf0KIV8H91TL343/q4h7EA0CLoDr688Bz7+Hoz0a5v6iziQTIB4AWIefoz152TW4N9xBhAOgv5KM/gQa4r2lbHEgGgDWAfPQnsDqwEmrGfW3dpkEyALTfTRaP/gQa4L7G4hAQDQAthuroT6Bb3INsAGgpso7+BLrDPQgHgJYi6+hPoF6wM08Y93JDUogwAPTECss6+hOx4RVYwCH3N0Xu3cHouI7YMIgHgNYJMNsSpT/6EzzVzv1cx30d1jDIB4CWucFZrXoQH+4e9yAfAACgSQscJAAAAECEAQAAIMIAAADAavF/wAnxuST9BHUAAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMsAAABUCAYAAAAsy8OlAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAoCSURBVHja7Z1Pb9VGEMDdC5fCEVUgNrcgeszbRD3RcoiMieDQA5QXK+ohkEMUWSIg5RCB4Rapae9wghPhKxTuVfIJWin5BMlnSPpm/fe92H7e9Xr/vTmMlDgvft7f7oxnxuNZ7927dx4KCsp0QQgoKKgsKCioLCgoqCx9SeT7T4ZRPG/TNcdRsED96Jnned8hTzNYmqe9owHJXCAhpXEQxQs2KvnbkD4kdPXPLjyQp0SWpg1qlZLRgOiJDMu15ZOXxN96afNdsesYkGfpjhiQ7S7Xb9yAQkr2R5N73HVy4dZLvMHRWhzfsFlZ4njtxsAjR8ubuwPkqZels3HKKvU+eXT1kwq30ZWxmH4Ncoyx91F0HE4qSmIFvTMavn3Yv6UafO3b2oK/Da6ULquuiqeq2EWUpbYAvs4i1/0tOzbt/zPf2vPIWV0gWj4Hz3llKUvVdzV9b9NiFeHJO2ZVPGWtp1Ysh/Ejo5VlZ2ft5oB4R6PBnM8tBu+jaLhAaRhnf9/dfHz7Pp37UPaNd3Y2rg0Dug3HhnE0n/jg3rlHBkd1k8dchhrrkcI6HZ3jgsmt4FsUD+ep5x2nx87bWlARZdkaLg1hshgDev/Dxt7e1WmLEb5ndH0nk+4DL88mlk1+vCqe3AmHhOVpznJn55ooS+OUBaBDvht+3tvbuFr2H9NBpICLiWGfYcfI2VIQvoDFlVmHqgHDeYNb3jeYNPhs1XWwzxDvK5w3szDJ7ZmcBmG00tedJfkO7wJSmCw7Ey49hexM02JsGhMvT16Wqnnyu1PyWBqlLJlGA8zsNsmOlSxhnRWbPNY04NxyTIFRLCZy5ofhb4tk8WDaop90N5hlB2XZ2blZ5YpUTtKE1YPULiHef1MXI/vfgkEDzzdNPHlYduT5mZdnnfTN0jhlKVsfuGU+3ty9XQWis7JMsZSVn224bV/KpIDbMi4Xl47R8GPtopsYW24hG/L/VYtDlCe3svDzPO3I85JMspHN0kg3LI5GvizxDvNFVuErq1SWzBqlgF/1mQ3Lr2vimrMJbvLr6yZYhGefylLieS7Ckzc7J5OlsaljmORgce59MsnNiiGsLC18UvbZkc8bBiQu+9u9KEuNNZwWkLaZYB6ewsrSmme4L8qT16Xvg6UxbphP/deQsWiyBKpiFog3sjilcGnIGc/TXR5lKX/HmCvVwn+u+pwoz75ilpTn5y48+V364vxdWJoZs4wuEiw5TDD415DBgFKMcpo4GUhhlYpjBRiYmNyyjIJr3mwHOychX8oTubu5PEjiF3oC/n+P2TDmosD4E0vondOA/gHjhWsIhvHPbTI4Ijx5WarmKZANk8LSTGUJwvUoWr6b+9mEHmZWtpSvLwK7IIzTIDY9Rk6DKFxJU6LpsWJxtHkuMB5YwvniharvbvNsILG69G8eCxX59Fn+XTD+MFph5wEmJPjaaN1LcYMIz3Fpx1IlT16JgqV1GSyNjln6ljTHf2ZraX5d3KCr3MQlnl1YOqks+TMIB2qZisWqsTbMIZ5W1YapEleqZE0ZS5dqXVdYOqssrr3PotsFynlWJAHs8jjIoShLZ5UFBN+UlB1Qd3vT0HaWTitL4j6QfVt9bdZoYaLWC3nqY1n8IFjUZoPY3N0FeZrDcjyAEyhqQ0GZFUEIKCiqlaWtG4eCYpP0ErO0ceFQUGwTjFlQUDBmQUFBZWkdN0VhsOL70RPe8mtj0rKj64fqWdPT9LazFuHsjKLAOxXQ9mcpjJ7aPhZWWkIeHJRf7DKNNbyZaTtrXs7OKAq8fORKSX42kezNQ8NqseA9mgeEHLj0+kNbzk4sLGiS4Eo5/mXLF3wxyc1xkXXOecodxvqB6ig0VBlPmFRI6UJham0M06JI1G6LEK/daNMcT/Z3qmgGXnZ7THAxdbDW4V42NdiYibuKzMbVIsrC27x6UtjbfZpfvNLBWvSuL8p6GmerLUEbiyu7cTWvsog0Atd9NzOFNbdCCzQK5+E8E8GvzMbVPAtXtHl1dWDtfdIVWOtizSOyWEMlSx3nmQnsRRqBV7kVbZuBd2lebZorJoH1ZxHWKhqF83C2VllELC1vI/DM0og0A+/SvLqrdTeI9akE1r02CufhbG28cn+OfhDx4bs0Audxw7o0rzYpbpHAutcm4bJZN3G2M14RXDhdG4FzKUuH5tVdgmyzWPffJFw26ybOWhZ71zQigzOXZJba/o+MRuA8i6dLI/AmS83d+V0fayVNwidZ8zYK5+GsKd6A2zM9EW16wOu/y2xcLZAN425eLVNZbGYtkA2TwtooZUk2/qTHwhP4+51fr1z5EZpY/8AXOHZvXM3bDFykEXid3Lvu/XP93tvtWWHNKyKNwnk42xmzcE6gKyKiLMhaHmdUFlQWZK1TWabVAlV2zuCoI0JlQdZOKAt7wk28I1afsxi8j6LhQnn77t3Nx7fhjcasaTcEhMOAbsPvwziaT3xs8DkHtc2wUVnks67LVKGy9Kgs7Glv2ioT0nflrQqKMgh4Ap6k9NKA8ALSfktB+AKCsGk75Jr4UpQKmXySjqzVcO5FWfJNb4bxo+zWzo6VrF12MZ130J1xZWlg/QZZW6As5YpTKJGGnHqVP6xyAm3sfNhmEpG1Gs69umGwJ3u+ISjc8iv8YcUTaF3nw7aTiKzVcO49dQwTCe1y0l1wG/e1R9egm3uArC11w3zqvy53yaiq/MQJ7D6JyNqFmGUEHip7YRKTroVLT8v7q7PaIVbgllSiFr8XRXCQEs2rSCv6OaGyIGs3lCUI16No+W7uS0ONTvq8pKpOaFygnihcSVOe6bFi8lFZJpQFWdurLKoEH0oiax2cUVlQWZA1Kot80b0Z7Swpi07WqCwdpdT/i5WLZIE1KosC1oPVv1SyRmXpINlbeJc6vHC2M0Jl6chakcKgsghK1sCgvBcJbISTdV5U2fgOJpE8jNddZg39hnWzruNsp7JEP/3y/ZU7/6qYQEidVr27LdrSyDplmUHWbimL5t6/zK9mDRHEurR0ucPZ0gqpB9bHKq7BuFZIMgYk2vhNlsCDK5V7ldjYZM9G1s412UsA8rcFkukuEI8eKt0XRmv71tlh7Vz71uzWrGMXKl3ukE2NwWUH/CpZO9kYPGvFqvp7oQ+Yjq0ftG85MSOsmzhbqyw6fOkqC6vi6bIJmxnNAmtnNzNS7R5s+fQ59beej+/VsnFNxSKyaZs8m1knnMe3DnFGWVRZ3NFCeZVv/TYpPS9ikzZgzTZx6lspdbBuw9lqZcktXo/+dNZguk769qlN2k6bbX/dI2s4vy7WbThbrywg0CxOV/Dbe2BNHhyY9OKVi6zbcnZisDpSjComsO1ejMhaDWdnrEPSkZHsl4vw8I6CrGVydsptYX5vGKz4fvTE1nfG4fr73AIbWYtzdk5ZUFD6EoSAgoLKgoIiV/4HWWlJBVXSKPoAAAAASUVORK5CYII=)
Now, using the identity sin 2x = 2 sin x cos x, we have
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Using identity 2 cos A cos B = cos (A + B) + cos (A - B), we have
![](data:image/png;base64,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)
= 2[cos(x) +cosα]
= 2cosx + 2 cosα
⇒ ![](data:image/png;base64,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)
= 2[sinx + xcosα] + C
Question 14.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Let sinx + cosx = t
⇒ (cosx-sinx)dx =dt
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATcAAAA7CAYAAAAel839AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAu3SURBVHja7V3NbtxGEube4wew4Z6bnbOnZ47JyRhx5exRWc8QukS2DgOBgH8AHYSE9s0H5wEsX2JfvAE2Vy+wygtIT5AA0gtk/AxSpkg22eR0N9lkc5o/dfgAm+KQ3dUfq6uqu6qd169fOwgEAtE3oBAQCAQqNwQCgUDlhhAL3HH+AUBZIJBvqNx6hQUlPzsOvZr7wT2UBwL5hsqtN/Aoebsm2yUqNwTyDZUbAoFAoHJDIBAI68qNBTtVQU/de4p+W/Qs0/2S/U10vY196RXZC7jUN64NnW/WXnyy3Ls/Js7FWlDXgBHdOT08Pr6Vv2dCyP/YPQ4ZXzxcnoz5e46P9++w54wm7jvfnz+g1AsC331AHGe1vn4T4q77ux/M71HHuYyvXVPv1Xem+yVrD+vPDh2dEmd8sR8Et6P7D2/NXfocrs0D/14UI8n21VZf+gSQPSXOuYxvZbgWBPu32TPg98vl3tgm12Tt4fsk4pvnTp/Btb2T5f0+883KS1959DvikD9dz9/lhPkFhHj45s1X0cA8HMM1Mjt6Ed2zFm40kDd0HvyLPWtBnQ905j+Bf795c/iVR51fHLr4wP7vEueM/w2823HIir3bNGTtCYmYkINeMbKFfw+vkS9T13sG/U/kEffDVl/6ApDTyBn9kePbivGNybsvXEsUn5xv1wK+rVR8A2uta3zb+gtDod11fmdESgdmPYMQ9wwGgd3DK7uMEowHKx7AKyb8ZFC52SsdZPJl5nn/npDJf9hAl3VfZBDOpOL2/MQTkieb6Jq0/5t9+VTUl6GjiG9gLWtw7VI1tlXGpybXlO0ZOt8ajQMITemYNCqzVmS5ZAZhLWzXDx7wswuY5XvLk/tCIiREjX5X1P50dlOD/2Dys52sPXXIVqUvXY6NGXHdCvhWkWvvC7i2gt/l3doGuSZtjyG+le5Pr5UbCCOKOYk3Dkam7drUVSg3dk+ecOnApL/nXIjr8DeCWEn0O9jM6NysSfKySYEWtacu2bi+XDfdFxso4k8VlzTvXm6Ja+H4NBl8L9Me03zr0uJVI3GA2KdfiSwL2UwpvEcg7Oj5m1YLDLQ7Gb2L3p0dzPB5dPGz55JARXTTxBO1x8hMuuW+bBNF/KlquQHflFY9yDq3oFWaa8fHd7Lj472Nx+faCte49pjh23b700rlFvroo51Tkfbf9OOdm7vu4hUQirkh/ow+gVkydQmyH29ynbhn8A74/4zOfuRJmbcMYfWSxdlSU74ZE7tMe+qQLe7Lp230xYrVVoI/lZ6p4NvU8x/nFwJqcu2TZa5lVjITbokUXnxNFXPrMt+skJMNQrLUzBATKXsPvWLxhKMZecHP6EmweG3JMNL63vQxpJvAgMCyt0vIr/xgsFVY9txGgteq9nBKG/6eXktJAx8JLEzwBGyqL21yM5pQbkq+xR9zaa6tP+5WcU3RnoQzLePbNrlpPF7C76lRwffc3dHI+SPZdzRx3+VjLPA8fm8SIZPP/D3hALvege8//Ca5j9BzRkhu2TskKbd/JwnUmtyvo2qP6N3E9YLYarhO2+ntxpZGfC0iaxN9OZrPHkF8Kx+sthlvK8sfXWzwje6c8lwqybUfWsY1aXvayDfd8arLzQbISf7s6ypen+C75DmzZtql3JA/yM0MNysvmiE5B4z85lVUboiWcXOFlhsClRsClVvzyk29QRdhF/yu97xys50sjfxBbua4GSo3WcZGYdEA0YN10kCQnN1BplgBoefzo9kjptzqJksjfxB1uZkujIwvYm6uOG7+pcvN5B9V00CQnF0hj7wQAbtWJ/kb+YMw5YLmuPlSxM0yifzoVgwAySbNXFYI24TKKxybydLIn2Fzk7fs2d5DfrVUl5tbJWdZ1wVRH6JxyVtNRde3nZyv4g+Oaa+5uZJwUHq9TKZEAzET+WpXGbcFYQYiCy2vNFSrpbrJ+U3zB8e0V9iw0PI5q6rVUlZgsyiRv4GYCS7ltw0i97PQctNMzkf+IGSTXQlubkyiSsutZCK/Wbdi7ROPHXKB5GxZwJbFKnKVLzjllsyANpPzkT89iqMlaV7ZpH1Nbq54buom8iM5B4IkpYUuPgCJIDE6qq8PsbX19ck//3sYHN62mSyN/OkL16YHmZxbQTkpITfHi4+Mm1DCKeWm+5uCm6uIm8dfN6bcQLuCNt0Z0VMsfd1S0s3okyT5mbhnkHQNZwuwWvo2k6WRPz31GkIO0XOV9cYUYsI12Mem4CYoOG7vm5SbJt2eK+p5T8MaU4ZL1tiOGyBJt+I2944/CDa29P82JizDPraZ6qltUS7RimH9ctc6K4bDjtGY5Q+iHZbb1PUPrBgnbRUK1BqDmFC+au02ES0508s6yu1oPp3HsYPw+D5WXBCJb8rVnn1v4qwFhL7SgmMFiyZrz3UPbFni7VRsM/IiLix4o6vc2mQZcRVgedzIDuJA6E4+NKhi6aEFbYjf+/QRTNYyWcJ3bDPbpNXCE503UOTfj53xWRsC0pGrRX6FGv2JleG5uyw5HVOM6k+AVcvhmAo3IKKVTla5g5884vF5GZU2378zm/nfo3LbonIrLJki+VuZkitgtrvz4FuJNZdRbrZLDXXRJapTjtxEuAGRfnPUIef8Fo3NDd12YqmDVW4wm7DyP3B+g+/PH/An1UMJlmgfWPoRwf6buUufwzU4qZylgcjOr5RZHHyf6pYaGiJCXiiOhmw7+jZhhcpMcnSiVTkPVbnBsyEgylxINkDpbMSUS/r+eEYKFwbY/psy57Dm36s6PVy31NAwrbbuVg5pU+jEFCKuqjMRULlpKre8OxdaY0CctZCVlQjYvqq4LlRyjbPcZO/XPa1788Ok56L+2Cw11CXER+4pq5VUCTcUhQNMhQ6qKrcy24l07zHVP+Z9tO3A5k4rN0my9s3GNer9IrOU4Ig3dlZlmfdXVW5sgUH1UdoqNdQ5l1TBiXCSiCu6wtgul3tjVbgBQg2eO30G/987Wd4XhRpMhg6qKLdMldqoX+/z24ngngkhnxPOC0IlMtnU7V8yMbfMNR2sW8pV+4wUooAMJpUbpD6V+QB0Sw0NCWVkrRtu4NJ6lKEGU6EDXeUG74A0JPaORBFxMlBVsuWtKZVsqlS63ZBNQQ4pKrctKTdeyUGSblLBQKHIqio30bYF2QqrbqmhQcXb4nCCTNaKcMNPKl6VHdMqoYOqoRO+HTx3IqW0ti6Je5ZUxxC1NbHGolgYa7tKNlVDI6libFfcbZDKDQYjzGHkZhnRFg0Tyu1oRp/S2dHTLMEPb+UTxG2WGuqMcitYvMmFG96XDTfojKlOJVi90Mlmn8osnshkkudQWdno9k/0LlRuBYjKnji/AelAYGV8eR3lFs6IcSoUPNv3po9h7xO/7SMkOGdBpdfSQQSlFFoTglkrCn7HcYw8ODKGz7VYaqgvyq1quEF3wuJDB7oxJh3vQlalVnSPSCZRv9IJu4xsqvQPlZsGhGlLuUUBudtSXIEgHAzXO4CyKulxYvScBfFFpX6I6wVpAT62MdHbjWM48bVUOSY1qiTgZ2ObpYY6qdxKrUyXDzdoW24lK8HWjwvHPBgvPsqUTCYGl4t3Rf3aXJzakA03KVfpH6/c2rQQhu4Oojcxt6rhhrLKzUToQEu5cQsgd93FK+ZlhJ5GvEAlWujI9IG4Z9AHhWySibNq/zDmhkDURJG7yD4ynXBD2VCDqdBBldVSLk53w2/XYDJI74nawXI7+bSnItnU6Z/OXk9UbgiEBJELL15kisMNP+iEGzZzIMWhBlOhgyrFG6HgQlwlh+1zO83nxYYliLi9cIRMPvP3FMmmTv/4fW5t4gp+MIhOId57hZuc2xQuYBkKLYsL4+Aguhh3u8Q9gG2bcFLXH5UbAlHHNe1wVZC+oa1VWnBwEB11g4pPVEJsy5Im520ME+AAIToJVgEWZWEXdSoio3JDIKTuKXmLm5vtWtD5vF1UbgiEKQsOT7+ypthsHdmHyg2BQAwaKAQEAoHKDYFAILqCvwEhOFD+o7JTjgAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
= -t-1 + C
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 15.Find the integrals of the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAAZCAYAAAA/vnC8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAARDSURBVGje7VnLThsxFHX3sIcKZxf2xMmyXaHBRbCMxMTKqpBFFFnlIc0iKhN2UQXdw6rs2h9oF/AD8AVUIl+QfAOpr2fuxBnmlSiJGjGVLJXBY/v43HvOvQO5uLgg+VjOkV9CTl4+3gx56t87HDkJS0Zey6KnirgXQmh/u9ku5UQsCXmu5FvMkofw/45ge4TVbnMiloS8jpRrjW53BSSzxsgtE529nIglkk2dcVo22XPdcd5P4pHL7pOzxBK7wSKASE5PyAa/h0yM9Ue7YlNCBupMQ+WRA1qqfW84zuoyEjdrLJEPBWNu3XXX5w2m222s7BTYTdxeowwdG8M0wv/HMQ8srx60m9slSkqP8yLPlAy9FxOXccR+ovRnRciDIFMF31WR2wfQy+SV88Iy9oPjNFb5BrlXXtQDLzLlM6zVYWk1nyVpupZKjDzK7+KiDqpSbrsfYyI4FnDa2ZL6zbj3kvwpy5xpsGTBMRYdnJI7T4/10H0Yl+4WkFpj9MpMeVOv4fc2ZyeQsbYri4LRS4+c0uOs+zivR1SFToQyNJvVUpnSP9h+AFBpsUMd4aFAcZz6eyUxj3DOQplfw7uMCddUIEbJA+ItsJ2bsD+1m9XNtDnTYMmK49WCUL7rzDMWxGe2dItGkz2kVuvU80jyA024wsUxLA7Rps15xn0cnAX3jfcUOoCgAe/GM0etg/0mBK7G4J8V1qK0/Bvf9SVuYPqTa7P9Aik8cSF3Mbv05U7gYVFYJsGRSl6QkT7jgVeFiIl8DyR4hsWFty97SPJjKSoH+mwq60E1ImXMra8zQnrMdvdRhvQzJs49vPQXXJophx4+OoA1EZt58V4AKMVR95SlXkjDkgVHpszD1AV5FLxyjEa7SPLwUuOAjM1L2de0CJC6arO9GZCIivG6MtQD/AnnTFtoYAGThCULjkzkjTyP9pUsfpFy+8MiMw81P+tl+V7SS8oAV9pFw6+G6M8eMfRv0sUGhYbK3HliScORTTZDJET52TzJAxCUy5MsHxJA/ni5/C0tM0aZZhd5uXDtf/HpCen5m5LEs6TqEfFP+kEjK5YsOFLJw4Oa+r4o8gBUy2JHzGodmf4DSmA292YJLTj/LDtyTe9tVGthSbKY9dWsDDGboBdDSd3gtQ7MwfWhSNGy6Xnmc9ScuKzKgmVSHBFfV6By9KscWMCTSK+KUofUvue1AtrzoBKrNpslrz/03sNSHIoC7BmnI46eGa3L+DACR8uLfxaUOx1M6sxS2ltQiET5CWW1K7x4+HSFZbtR8YX2HZX1sXMietesWJJw+K3MeSJ5QclL2QMuEPQY0N8xcSldJTU6Ommf1euHfqS+jHpDsetH5kvwAXrCLzZjzXxM4TA+V/mx8QVDl/vqzHDe8GVq8rjQgRn4noEX2wOzhzNbB3NOoUCegj5P9YtRJX1WLJPiyP+0kv9JKB85efnIyXsr4x9a7z0xMHv1kAAAAABJRU5ErkJggg==)
Answer:tan32xsec2x = tan22xtan2xsec2x
= (sec22x -1)tan2xsec2x
= sec22x.tan2xsec2x-tan2xsec2x
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASgAAAAxCAYAAABpqTT+AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAjdSURBVHja7V27cttGFF33dh87WnZyanOpMq40NPwqlZjCqPFDBUeDGduaYaGxIXcq7PRWGjtNkpnULmL/gPQF9oz1AyF/QVJ4ASy4WGGBBQmAIHWK0xDQ4mIXe/beu/es2Js3bxgAAEATgU4AAAAEBQAAAIICAAAEBQBAwyYzY1dUgKAAAGgEdnprPc7YaExM54zxEW9v/rY9GFwDQQEAMFfsu+LBmJjONJyzFefLopMUBhgAFhgHB9tX73L+15rrPZK/PXedu2NvakgkJdz9ByAoAADSJ5iWE0rLDeXljrKu+55zy+n5t01elSSotDYWIV+FjwgAKsJgsHVDcHZERNESdw77/Y22EK6v3rPXX2/Le6L7flfDsr3+xs2s6ybsdPlLxsT3Ld+/TiQ29qj+C/NTYejn+b1Vwdj36Lezpnpa+JAAoCJsCvZRdL2nMhRzBfvAxOZH1cvhvPOp5/mridAsyh3R9RZrfXVc7570luLrBwdX857Nuzsv1VDQ4exzEPb1/IfkNYVeFh/K9i8NQS3TNicATAPf37pOHookg/g34b6eEAb/e72/11ZDLSIW2oVb7/dvOyvsi04yruBvGXc+k2dkfHZAZOJIv0faRO13XffXDu/8mdXOUhIUuaxtzo7H7uWJXBnmHfcDQN1QPRYKyzb6ezfV7zHyhkYpu28BRLf7iq4XDb1k0tzx/Ftm8qIEOpHgXrvp/ViJWxt28th1NHRSTR/GGZHk1mBwAxMGmIsX5fVWlfzROePtY0kKIVHwbyaSiJLcQThWZGH2uuJpHqltCv6ObBp7Z7tNX8TLd2tbdw7z4uMqQQMkiTGI+S3idQCoypOXROV0Wu/VRVN6MiaSiD2s9uYftiRCiXHueC/SbEi0K9y3rsNfB55aAQIEQZW+gtEgt4+bHmcD1YT48w7xuqL7St1xU7f+1RBwxdncp/uk3X5PPBRbW0/lLpt+XfeS6LedrngmujvP1PTGYLB97U5LHMrvn3YVZd5p8vxmh3pLTQhEmG3WzkwoLqp+aZF1V1XZHkzUXvc+5UDV5PK8CIoIgIvNd5JcPHftkdz6DwhrS9yPw78EwnuUCvHkde58lk5ASE5UUqC3ESHaNSSykkl5aSPli8M8mDjZ6A9+asI3oH8PFRAU/zaP3JPJHrnNm+oSl6xfqosoFll3VaXtnsNfyAndCIJy3Meet/5znIfi4kifG1RaoNY5qWUH8nqrxb7GdVAd5716PXrnU2OyPfK0gnSHkhtWaqMu3FsliCiJqNV3Yq3W17XeTi+oGxOunyCsZSUoeknXcZ6Yws1M/dKUIaorhF+191iF3XWhDttl7mbeBHWZcmy2oKLTcIefD1Vpzr7n/RDn6DT94FISlHR7TStCmn7Jc517s+iXQne52vC2Crvr9CjqsB0E1Zz0iX5/VINl3N2PN7WqJajs2o0ytEl5MeyYnHbl7gi5jd2u94tuZ4Z+6byofimI71fYF7lDcyGO1toxXTe1X9TuIrbbjsssY1JFn5ueqxPUomrQlo2gojzZWdbCQW12Ws77VIJKm0QmTEtQRBahixfG0pbapEM9R5GiT4rvmcTaEvb1WCn6paGamEzTL6m7MfJ39ZlEXrLuJM4zKHkXut5zxAvyvnq+txpUCgf5iknNTBG7lXHItV0dl1gzljIus47J1H1uoRlLPJeLo95O974kqGnaA8onKLWCPe+bdoV4rbaZdK8MibbE5NLqLIoQVFFtUhQCjNQcBW3BBmFkUp80KiOPkadfmqz4F/VLYYHq2IPSBkz+Lt9J7rjI5yjJy9Ga4z6nd4jfSembInZPY7tpXAxjktCDzUszFu1CDeXfK4WRcf8uqgZtqQgqXiiKF07XFuJFLHoyrTaJPJLgnin1SXY5pOn1S2kEFU+OaFuY3ife2lXIR/9b+Z42E9xkt63tWeNS9ZjM0udxH2kkLkNG1Z5pNGhlRBTLlhBP1liNo6ExQW0MBj/m9cdkc6TBBKVpkw4La5PGbdrkuKZN4NJEzNEvjeSkNHkCaR6UHFwK5Vxn7XkccpRAUHm6q+TqlW57lmasyjGZVTNmSobn/G6tQbOOKC5JMj7qj9MLO7B6nwj3g05Sk3qvGQiqvByUeRfPRpuUNdnSksFlrAxF9UtFCGqSg+JDCuGoLqYMD8rWbhvbTeNSaExq1oyZvoWsXby6NGhF5lJTMa8clJGgystBmT9oozZpkiAdZX08am6mrA/MRr8UhCIT/VLqZDSGeBrRpOWXpiEoG7ttbTeNi+uFOUCrMSlZM6bZfUEzpoRyuzYElddeyQR1ajOXGo4rZe7iRfxyXnRxqCBxxo9NoYRBm3RupU2icCJm4nx9ks0qV6Z+KY2g0ibLrARla7et7VnjQjVLZY5JmX0eP1erm0lb6BZRg7ZMSfKUEFukkVSYBnEep+7i1UFQQTJV0SaR7CGhTTJpj2zuUfRJduTEd2fXL+3dTK4Q4UcvK9gTu1njdw4GICwjCJ5BO2Ib/X47rKGaTJhg25+xEz1mt7W7iO1pmjF1XMoakyr6PJa2jL032b/kAcZ5s87df7b97eu27QHVEZTMRYXyGj4iaUtiMfN6tzqcf9K5o9S4mz52fRVPEJTjPsnTJtGkzdImyXuy9El5UDRb0+iXhmn3xte0d/KctSfybyjEoDqcaAUfkmJ9cnaVfI57L/JIot8mRGBrdxHbbTRjZYxJFX2u929Q7zV+Dyp5kCUbRdsD7AlKMPFv0Z1zkrXQIp0cAz4MFsgUB6NEY9mJcN1nQbiA85cAACjD8SmjESWuHzblJAMAAEBQAADUOWEvWZEoBh0AFgSLfA4YCAoAlhiZZ2ktMUlh8AGg4Ug7Syv+J58NPwcMBAUAS46cs7SWukwCHwAALCj0c8BAUAAANAZp54CBoAAAaETYZzoHDAQFAMDcYHMOGAgKAID6J+wUJ3eAoAAAqAW254CBoAAAqNVzsj0HDAQFAEDN5BT+N6C8c8BAUAAA1IroLK1Tm3PAQFAAAAAgKAAAQFDoBAAAGor/AfdU7MYWcJTpAAAAAElFTkSuQmCC)
Now, Let sec2x = t
⇒ 2sec2xtan2x dx = dt
Thus, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 16.Find the integrals of the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADQAAAAZCAYAAAB+Sg0DAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJHSURBVFjD7ZexTuNAEIbneugPxJR5gHiSki6KVghKJJyVq0MpLLQ6QuEC6TbpohN3z3A8xRXwAsczwBM4z0BuZ9ebmCSccwl2YaVYJbHsnflm/vnXgdFoBHVatYLZAX14cIBPtQLqEdyTHJ7WAmgo6dR0aFoLIK2jAyKpa9MhSaQjrQ8qAypjWGfdCemMQn3GMSxQ9r1UIF/Bj4YZj/t7AuHBALxma8qfKNSgNKDbuBMgBE9lAFXucknS3xdH8AhAL1GSHOalwN8X16JM/bX37llWAvxaF6go5hJQTg5TLwUATIXSTQbtEf7ISeUVg97PfpLs+0KEggbc2VCrhiS8s/dh8NSJb4Ntqx7H50EL8TdQ796DqC5dIkAKKB764/Heu5JjGdgO5STnr4VKN/j3VRdvGBq7Vze+0q4IOGkLec0BtBJNE3Dik9jyvMoKiRMuEM+4z6VwhhaBZp3LKsHVcXP2NtmVz7F8j8RjvoKbLiXbFzam6TqrZm1TWNUh32aWlhTta9tq7kiFQOvutxbQfIYwNZL6qlTnuOoOzaW+XOz/l9xCYqvmo2wgfl0SrdZ3jvsvZywE8sl7A6gSKG/LUogvaqg+2z1zblcI5BwrcxPexMkrtYkZm7Zz5GzZzpCS4uQ8jgN3frnnnEyjQwJ48WfaxhLLYngjsIUzuSgVNs0L7rdCoKz6xt/pj99k5vl8/pC8UzpsuDMLU4qiy7evM3x2yRMD8zy/Rs+bvHkogQM7t1Jd5G2cc+E8VnV+9xd8B7QD2m79BSPXQio5e9jaAAAAAElFTkSuQmCC)
Answer:tan4x = tan2x.tan2x
= (sec2x-1) tan2x
= sec2x tan2x- tan2x
= sec2x tan2x- (sec2x-1)
= sec2x tan2x- sec2x+1
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, let tanx = t
=> sec2x dx =dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 17.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= tanxsecx + cotxcosecx
⇒ Now, ![](data:image/png;base64,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)
= secx – cosecx + C
Question 18.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEQAAAAxCAYAAABj/A/AAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMpSURBVGje7Zq9ThtBEMc3PX4AEOMOem4uZTrrWBEonei8ogK5sKwtAOkKKxx0LuABoIIqSpE2KeAF4AmIhJ8AP4Od3bvb8/oD50x8jmMP0gjrtLfe/c3OzH93zc7PzxlZzwgCASEgiwdE/b3TtvRANIS6733cxuI1Y9jaD8PVpQYiORwVi+xJgekSEMsqyG4JCAEhIASEgBAQAkJACMg/tiCoFrjLvmsgpVrDyXtPM9cwzgTuKgCdPkNxQ9t/2v4TkPkDYg5hsthSABHIboYS2AgDLo8oZCiHEJC/ziGTvD9vlksOyfLuvNrChEwele+/hdFsVlc4sLvYy2rjFwRrSw1EenjIZbiVhvs6v682mytUZZSFkm8Bcx6ncTywGEDC/VWHOXcExFoh6MlDEmZJpRGcH0wjfyxE2a17cIzibHfpy24C4wS8+on+HAT7a54nP80tkLfI/Sziy/wfVtbwYsrwa31nEXK5wGjUypsI7MEMtojb19UgKAy2cQF+phMC51EfIttttNcdYI9RHy6/qtXKDqIIs5Vh9hL/jEIZ8DsZ+hvI2HPyrPNamE0/4/u4Bwx+cSF3rMG1beHUqJUc/czsi0KpBhsD7KIf7pm+9PWDqR5amUarAiu3EyrZtM/40FqtpGRsuQOJBrHO7lVcH9vPBMKF9pLWCabNoLJMwSX3L1pbKI+29GTMEo+eoTidRJ/EqwLanhCfXXC//kmr5KAYWXtc1k8nPuDpFJQavM4Ftod1yJVrjc23bOJ6oON+Z5pUk3uU7jggps2opR/f0PXet0KpE+eC4TyTxSoIl9HRhapIMwVie/81b47KKf1Aep5MQ0WB4W7xKt3ZTiDRo3yF4kJwOB3MUfkDSWOWddd55UxXFlPm9O5Ue35UsosrSrUQhYzKNRqUbueh98WuTllW4GCVMnmj973QHrfKpl5lrOvHbp8lE+1vgy2TG7TitLVEmqCxcmnA1v33vnrnOcsKiQADfLMnb6qb+d6Z6RAp+E7yc8qO0RC+DDeGNmSWVgFwf9htIiBcHEhZ+pC2A3zIkhj7hVsM2dImqZgbtdLopJ2AEJCJ7DdbGpPkE6+25gAAAABJRU5ErkJggg==)
= sec2x
Now, ![](data:image/png;base64,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)
= tanx + C
Question 19.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPQAAAAxCAYAAADtCoT5AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAcwSURBVHja7V1Nc9NGGF7nTLgTsrpRro3X3NobI2/46M1TFE0uLfXBk9GUhBkdMsThlgO9k3IocOmUmfZWZkrgHuAH0JnAH8D8hMapVtJKa1sfa8eyZfs5PEOyKNK7z76P99135X3Jw4cPCQAA8wGQAAAQNAAAEDQw2cElpOJhCVxA0GVzSjjmCNhg9BdC2CfLaV8BH4vhi6UncMsyb9aZ8UQ45ma7fQmOpQ+b0UcebycQ9OL4YqlJdDjdNgzywftI7ELQwDTRmhFfnJHQkTyDoAH4IgQ972HgUoiKDAsT1nxLaW3y54RrllQktFUgaAgagh4jXHdzhVHy1hPXqVHjh61Wo8qY3Y7+v9W4KtZ7lFTfSd5ct7lscbYt2hq7ra+CNTY5JbT67nprtyquaTt8jRLymfihJTkjlB85besKI+Sj/7t3PbP3b0HQEDQEPWZOmOncFT8fHDQv2Iw8JWzjmS/K9uYlT4An/es9y7smaKNfrnH75+bBwYVQwB35t/J+65S8EgJmVvu2mJHbFvP+pZ+57dxAyA1BQ9BjRCjYT2vWg+9k+Ou3MXsvj7f+NiFevkpek1X+Wgi87xknQvymbX9fo7XfwT8EDUEXAF+ElByJGdRg9SeNlns1aW/0PIJWwu+OELUMySFoCBqCLmKWdrx1LSXH/hpYhNHBOpiNU9DB9eLlFNKl5tb9RU6GQdAQdLEDJ0NtT9i8ZhwGwvY4ct2VcQl6t3W9Spn9yOZ0T4harqchaAgagh5zyG0y80HTdZdl277NbvlJLCUDHfGWIfI0QYssulw3xyG+H3ozCLqXUwh6iFmo2Wxc5Iz8JUgUzuT57MKHfVJgYvZsNJsXxfp5y7pmidc8pVB93lbJGyFymTyL2wJhijbXbVwWCTbBb8N1Lwdibi5zSl+o4vVmay/CJ1/864I1+0KNg+SvXiN/xr74onTvdJeaxP1NdjNcI8Zg1lMI2hM0t39wHP5NtI6m7Jg77bUgDI/2kiPeKLf3wq2osI1+5vfs9SCTLduCDwSxvRVd490z6X6Lthcd+uJ/ZfdFrEeBac56+AYdBA3MA8Q+d5VUj5AXgaABCBqAoCePM+XLDzmoQNAABF1yxMmlbFDubEPQAAQNzGy0IrbLhKDFVllvtIJtSQgaKD02GPktITrpYluyQEFrrveABBSxhp43PkYNueFf+lz3E3cKjIYi1tDzxsc5BA0fy0YFIXevw1R0ZxZwgaQY1tAlx5ZJd8JXHTuL/r3fSXEBQUPQxTiWw9eucefHyJmVo3jARXFcBCeisH8gaAi6MIivIC7injC4WHBBz2NpGvHVONO07uJUjtnlAiWTRhT0vNVMUo+uFUftLPoSZFa5QC2vEQU9rzWTROmdtLO1Fg2zyIWFWl5YQ/fMTiJRY9R/haDBBQQ9qwQo+67iMPlFTgSBizkVdJlqJo3yiuQwffJDy5T3iMtW4wlcZPvmPPnlqHwPNEy1ZtLm/k11IMSzpC2+PeJQ+WbzYo+93jU1Sl9GjhieT612OK9PeckhHXuLnjlLz8UEzhjLsn1Uv9zf4V+LvlUG+3aS1LdJjIXkW9emTEFvVMnzMdZM+tJfM0lWfBismXRvvceJvHaDGP/K9qiKg5Ko8c+N9p4hQ8Pw8Pm38v46fcrCMPYWup7V56KTy0VGTaw8LmS9K3mK6KTrXaXZnuaX4htew9byyutbPBZB+xBjcSzvrzMWo/I9mAgpQc0k+bfU3NpR2/xPWLr+KjorOun+8oMktEW3T5nJoSnWeBoDF5154ELH9jH65Z1h/NLPrtO6/li47kr4vI9hf5aS+qNjU6agy1IzSYoyK4xLigB6nuvdWxxBq9snjZBzKjWewMWAb3bTbD+vX4bhd3F+GRcrqCozcDdrLPJsyg25y1AzKaoCoYSKAx0Nr0kKFwNb4ioSOn3KD/emU+MJXGT65nvV9vH6ZSvNL7saY9EdcSzeJ41Flk25gk6tmZRB0rDEJdVMSvyUq955npJhr0TXrPI3akmY2JZgVtLtUxby7J3EDK3BRedcXGiWdlG5EOtTNQSeRHJQsf1xv+3j9MukvvWOxVnOWJhpY9FJGYvHSWMxLN8DYY3JzD3tmkkjEKdTM0muL8RzV/nGviz34pd8MdlPIrvcn7CK799c9p9L+ZF4rm6fsjKr06zxVAAXD2aRiwzbu9L2omt5xWtavbFQE2BiLOp6YxH1p9+mIETP5jtxnVKGmklKGZwzBV1JSO810d96xNL7soSLbp/SHbgcNZ7ARb7tft0pP1/Q65f1MIeg65eyDwX45c4wY+F/AFD6h45N2YKeds0kZW/3ns3XDYN8iPb7avyw/z1dcQ9lHXJqGLW/1Wvy+pSFYe0tEjPBRYF70bHt17/ttz3NL+v9funYN5L8Mj7AUK9vOmMhklnqWFBae5k8FoP9kVtuo/CN1+UAYI4AEgAAggYAoIz4H3bOya9kcuQ8AAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
let tanx = t
⇒ sec2x dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 20.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
Let 1 + sin2x = t
⇒ 2cos2x dx = dt
Thus, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
= log|sinx + cosx| + C
Question 21.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:sin-1(cosx)
Let cosx = t.......(1)
Then, sinx = ![](data:image/png;base64,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)
Differentiating both sides of (1), we get,
⇒ (-sinx)dx = dt
⇒ dx = ![](data:image/png;base64,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)
⇒ dx = ![](data:image/png;base64,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)
⇒ Now, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARgAAAA/CAYAAAA7UNe2AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAp1SURBVHja7V1Pb9RGHDUcOEFvqIIyewtqj+xsjpU4oMUJcOhhaXetqFKBHKLIKn+kPURlw40DfICEC3BpkNprKxHOleALlAr4AiRfYZN6xh7vrPHYY6/tHXvf4SnSbry2x2/e/P6OrUePHlkAAABlAIMAAAAEBgCMnECWdQLjAIEBgMKFxXXsVdt2e+uPH59epHu/69grtuOu6ogryAIAGTEcrp+xO62dZcf9aVHHYOTalwhZ2VsfDs9AYACgQHFZIWTPdkeXFn0smMh0SOf3teHwPAQGAApwiwaUPKXO9nWMh54lg0ECAE1sdsl9Yrv3MBbTcG1yj3Q378fFZDBAAKCzUo/WznF3YDQ6h/GYxuPH66eZ23hlY6sNgQGAvNaLt0rXwY2bR+p8e41es+jgRfTcIA8AaKzQNiGvTA7ssom92e9eaxPr3TyEkFl41KKvowFfEAgA0iaPCGQaXO/C4iCeyIw9HEcFpiqLxqHWc9of3YDAAEAD3SMuhJZ1GL1Wh9JRFbGjbYdej7pJIBAApGBArRd1SE3HCczWxhXPa2q/q0JgfEvPfiWnrEEgAEgAi79cbdFdU7NHIqjLEBUYXnF8wXpjWfRTbzj8pmxXKS4OAxIBQMqkaVvtfRMFZmujd5ES6y2PvRD6tr/ZvSYExk8dW6+9745YXMb/Sw7KDFSLdLV8DpAIANJW5dbVXdMCvL7rYx0Ia2Xk9pcCsZkK8jL3jlkwVQkkq3TWEph55dN1TUKQ32w0hT9hXKFkgZFdnTTwtDlzfejghfwbPMjqWSrGCwxTR5ZPZxfWd0dLJpFj0LZe1iGiv8gwmj/ehMvCn6oEhqV4gzTzURLYtauyRXGfVy8w0wFx5T9V4bNlRZDrP8pCkLpYO02yygL+jJvAn6oEJgsCS+U4WnNSC4Ex1ecUyFKTwDcF6nZvmrSKqkhMu+7tJohMk/hjuMAwoXywcAJTtu+tSxB2DazAqC77djDSEDp4mmfsTIp3NIU/JguMnw62PloX7DdyzYkkMA/EGIYCMxyer4Ij6QLDLzJ/YQ4L8uT1vZMCW1kJ4v3fg7q11gdt7w+yjNc8+0+UE7IB/Anv5+dvfzh16rsP3v18bRpXeBijPXjZW1//SuyyxwSGf95Z+YOJoh/bIYes09mx7VtlC+Xls9Y/Zy9v30sRGPJf3pXfoeSJR5CPWQniN5RZ+7HBLeo8z0KQKqsXi16Z2hZ5F9f2nkiymP6T+QrMXPkzzsMf1epuogUzef7LtzxB+ezXwdj7rnvl+5bV+nfZdu6K6w2sms+sTqYKa17TgslPEBN8aG4WRlJ4dQFfcTJcuyqjUFeBmRd/VP06JguMiai1wHCXgLk+ko+pmnB13dbQD+DpB+UgMLPzJ8nihcCUIjDJEzTq2051T8YE6aL/mzeQJ7kER6r4CluhmM+ZRnCVj677fdI4xB2re9/h+EdSkKrzRgVmlnMXJzBG82csp6rT+nUgMBULzHC4dj4oST5qdeydjY1em1Jn5K8EvYtXaeuZvBqwB9i36T32WX/kLvk+ticSpK0da8h6g2kWgNTDwcWqRa/uytF49n2HkL9DHz7mWlXjEIzfQdD/ccx941F/iUf9g56QpMkXZAg+qdykpP6TWc+dpZo0r8BI4zZW8GdXxZ/e1sbFIvkTifvF9utAYCoWGP4DXfe2eEAiZhCmzvhDmkzwoEKRPbjDZdv5lT0ocY6i4yRhCTVL3ykIMerTGy2r9Z69OEq63wNxTNDjcSgsJLnHQ7YqVOMQIS4/hlsa3nk5eYPz5rmHsP8k5trEijzLubWrSROycyXz567En4Oi+JO0KEFgKhQYsboK4oafUedh0sOKfqYjBLnMc7H6K35XnFeOV/gk91ZFb7VnFlbcdYWCGNyDzjhMJgw57DrOj7obRodjExnDlP6TqSxS3nOX7SKZyh8IjCECI6+OnlvxrLexdTFqLs9VYFIso7TVVXX8ZNL7sR2dcZiyjjRiQqpzpQVzUz7PdO6yBcZU/hQlMFlczLqiIIFRZwEkszw2PmGywIQ9HAqBEd/HHR/014THpo3D5DhWOOaXdes8IJXAqK49KYuU9dzFxWDqxZ8CBSbVvWwATpQqMKFp6xGFVQ5GfWYjBEbxu+H37cHLuExF0vH+PUwmfdo4hDET6jxxbPIwrjktj8DoWjB5zl1cDKZe/IGLVKWLFFSTxhGEPdgu7f4mZ1yiK6vJMRgpkHh8wR5ss/sQK/Jml95hLzOXA6STzEeQyiT2PvtdnXFg2RIR+5i4Bn7Jdp4YjKr/JAxKS1ZK3nMX9Qzqxh/59+eRpm6Ca1SYwDCysqY8MTk3+8t9VtrNHs6kpmCSwZh8NiE4T1UyIQiasKrMIolO1DCVK9KTgXhMvqefRIwgqK0J05da40DIK3lCCyEQv5vnHsI6IM+FY+eN7T8ZrZ/Le+4qBCYybiez8sf/rFj+JPXrVCQwx3V3jbQERjxQ1SbHnCC28wvreQj96KDHQarBkExp5+F0fxGbpM7qJB3JJ/LHIjMcOnUwrmOvtlrW+7AOpmPvyL0vfPsEKU5ASOcv+fukcZh2NXxRksYmdD+UgeaUOpig/+Qg0n/yXpQAzHLuIlbijPwZR/jzWb5OiT/jCH8+TD6bnT9J/TpVCUzjXaQwheg4d7gZW1Of07dAqs2cVJWFMfq6G8KfqmMwgQsybrzASL66UbuQ5Sf6YvQimYKm8GcOAmOE9VJUO4nWlpl1R9aOZNNWAHl7AQACU93iwNzO2eJaCyEwvptB3xYZQK4CfvCSvG2SBQCBMV9gWFxvKn4YyVRCYGIHje8OV6u3D/C9Smq2C1/jBcbf0e5jWTvamRbgDXckzLk4p+5o1yxXiTypSyyGZ66knhzAKIEpZctMEwO84etfc8YAF0pgfEvG7tXhrQLLtnsLE3qxXKQ462XeG7jPysWFcZEAoE4CIzZwZ/vhlJlFTBIv/iaOGTcGh8AAgIECw2KGk+LP8gRGtfewqFgX4pDXimJBYggMAMxZYFTxlzJflKbaeziyV/FJls3sdt2b+SwYjXdTAwAQCExJb6pUZY/KEpikvYe/7KLPXywJgQGAjALTttr7RU/4KgWGFdKtEOt10t7DRZ2HNdpCYAAgw6RRNW9quEAnTLFgyv7t0NqLpLhBIgDQMPuz7KUTiIvYCuRkUQIz6/4tpQtMTLwKBAKAFGStCpfiGccJtS7jrCKgveOg4lrLFhjeqBvpowOBAEBnZaaDp1mPC8TgCysmqT2gzi5StAYGAgMAGuDBy1ZnJ09/Tpyr1ESBUbUYgEAAUIKbFGPFHGcSmBJ2ApB/u+h2hDj3CAIDAFlX6HxWzJSrpBIYf49l608mAlc2tmjRIpC09/AsYNe9QsheXNob5AGALFYMHTzNM/FlVykuwLu9Rq99EcAteOOxpL2HZ0HSNiMgDgBksgLIE513TOm4Sk0Abz8gK3sqawikAYAM8KtiyZ54hUoekWmSuKS99xykAYAcIsMsGfaivjwi04Qx8Ivq1JYLBAYAZsRdx16xbbe3aK+V5fftuKtaggqiAABQFjAIAABAYAAAqB/+B5uwXVMzKO8iAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
Let sin-1 t = v
⇒ ![](data:image/png;base64,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)
⇒ ∫sin-1(cosx) dx = - ∫vdv
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
…(1)
We know that,
sin-1x + cos-1 x = ![](data:image/png;base64,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)
⇒ sin-1(cosx)= ![](data:image/png;base64,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)
Now, substituting in eq(1), we get,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAABRCAYAAADFN4N3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAreSURBVHja7Z2/cxvHFccXbCO5chGZ3Ksie8ZVhAVKz7jQgMvQSgc7hwsaU0LBYW4ikTMoZBFUp0JKHcpFZDeJPWnjmZhSL/IfsDISu6QR9S+IzO3e7eFwuN8AgV3gW3xnSJDA7S12P/f27dv3yMOHDwkEQVCe0AkQBAEWEKT9BCSk5mlFCLCAIChR/X7vKqfkyAPFe0LYabvfXwUsIAgak8ubW9wd3BA/O4w8I2v8ee/RoyuABQRBqRq4/AYl9ZPuYHANsICg7LX7SpoMvZ9axj3VxmAx6F5jhP0MWEBQ1lNVThRy6q/d46Jvlalu1hKD3ku+H3JOWzu7SZZFk7tbWgMQgxXSARZ1Uj/S+ak6LR047Is4LISl4XC+pbO/ArCAAIs5w0KAYqdFd1n3YFP9DlhAEGAxAosAFHve73vCl9Hvt1dbLfdLwAKCAIsRWHQY+ZtJ/hkMVgiwmOMyxCRhsEKABWABWECLCYucGIYVnZ2EgAUEzQgW8jxFwzpUMQuRNf9F+DvlR7puQwIWEDQjWDiM7Qsn4KNHvSvrFnsq3qOCukyYhIAFBM3YZxF9j4IFcw6+ACwACwiwSIeFPIRF3gEWgAUEWIy/x2a31JFuHxb0PyacIQEsIGjGsOgw8h1hne/UBCSEvru5fb8uBzV2QwALCLAQur99sy6WHWrS+bAgF6y1c6fXa3/QYq0H2A0BLKAlh4XYBeFr5LnYJlU+ioMu2wy2TeX2KeXuPVgWgAUEWFzZoORnQtlL9f8SICr2QuMYC8ACgubgszBVgAUEARbF7tVmtwALCKoMi88//ZB8+N/PB4NPtZ4sCedPyp5J+eNvyI+/Yn96AlhA0IJaFkHg19vQkUr5kTuwrzNC3ijHapGgMLHla0LwGGABARYTKHSuenC4YT/4vbAkZHCYSFrjuL8r8hmABQQNTfW84+NjJvssYVGlfXGwedbEaxEE1nKcrxq08feywWSABQR5skVlreQU+COKxkIUhUXBSZ5Zc6RK+1KWJGfRqFHAAoI0WoYUmeRxXVabO4w+CWqA7JUJLwcsIGgJfBZKMtycOY8dTve9Nc258l8AFhAEWITq97sfKT+FjByVVdDlcoQBFhAEWASg6F3llP4QBYM61EYIO21v9z/JszAkLOzBLcACgirBQgZl/U/3oKxhnQ+/vkck9iL0keRZDQjKgqAlgMU0BFhA0BxgkRAzUQMsAAsIsBgDxY7dtH1/gQi3pu9ovfOXdq/3AWABWECAxfA9Msx6JKbCP7Oxxl/0+v2rgAVgAQEWwRkN+o+m436lXrvr8A0/qpJc6Lw1CVhA0AxhIXYhePfgs/jrQS7Oc8ACsIAAi0zttOguIeyNzvEaCwmLtIM4c2+w7wGvYZIBFnGJgCedk/UuJCxEVFqdkhMRlWa7g+s6gaJTJ9+bmpYMujxY+JGU7Fj3KNCFg4Us4BKJVNOlsS6n94KTfoVhYYoVsszW0qRp9UQYtnB4mlCRzIPFDwsDC5ncw1p/qms6dbEuLQoLMQHdVutLnayjxMni8hus5d5eVmBMcjbE/47ZbdY92DThXhcqu/eksFBRdfOGhWiHw9jAhKeNHERdtklZ50lZYESiGI0FTVVYyMAsMR5ifgqUL5wVLOThmPpJ1bWfnxSkmq8jI+VZrSwsvP/b093ZlbTMEslUSk0Wu7Up/Esm+3GqwMIHBbsjShZGx4ooX7husae6+i50gkXKfKulATcFFtUrUjuMPvZg8bosLIa5ARIyHjHnWRlY+M6u6sCb76ShJ0VTtQU+HNFHF8sEi8Ci2Auyao8rMl4Ai3Q/jwiXtyzyKpxnlvWqae/Y/X57lTFncOmw0MFnIXZMdB4w2bAlz1R18KL+jmiR4GWARQSSidI5KOsyYFF22XV/u/2xv9tJ3zYd9w9h21z317xh/VVk/yJr/Hk8bN4oWKgnSlbeQ5WMxNRsRH4UIjstOnGWERYma9qwKNt3ItMXI+TUA8VZ2hyXeTuKwyJ7smWtb5IcnNHXouukKmv6vOzLfhQffZcHu7yjzfH1XJl+mKRyVdj/GdmUop8Vh8U0qmYBFosLC7V8y2qD+MyGxQ8nhoUkEyXHYsJaDX64vd2uq/WNMG/WmfVt1F8g1kY2Z/fEa+372x/7Pg1R7bp+UjaNehH5MSLpT2YxWUQ71T3I+2Dr30Y7pr/d/qRB6U+haeu3lUUnWlo/FKpclbHNF9SlOE1bioi2hW2n7NjeaW0qWEx67Ulrakw64Nv9/mqRdP4mKK0vp13rtAwswrFV4GHqMLYf/8zSsJA5BFvu7YeBU1KtsYfFV8RAHU5Wx6/TcC4a2OTOn8WWrLpGmbV5EUkn6Rp5Lk2olK1f8WVZxHrFnbsbkfs9U+9RyxhluQxcb7L5k/Mi+rRP64ewHb6zVr6nTOWqrHsI2naW1DY1ACe5tjOFmhpVB3wwdhKup1dgYBUr+DL7rxQs1LwrscytDAtFJjUIw9eYs5/1ZI+/VmRSTzDoTtM+V103SnZ/onvWjvcUtgfu9aR2xTu5SD8E//OmbOWqsG9ifRi+HgNscNJyxKysem3IPItF7FykWGW1ZH+YsDBnAIvoU0uY7kE245W8ZcDMYJFjseRZTWnvH05g33wr0g8jVkuJylXxa+U5MnNer1Q1a4KBvAJNV4nOx3Fr5Xw83MB+NgaLLtsMLf9+/6MpwSJ9NyQwfV+GjYz5HnSGhSJrmvMwJG/C+4PzMmFilbx+GL6vXOWqNFiEbY+BLms3pOy1J/VZVKkYBuWqNmWfxZuqD5DSsAjNbm+y8IZ1GPdRaAGLlM8N/17vfB//EuTafvj+sdRs/j0MJ3BeP4Q+hqBylXQuFqgXkQeLeIRnGiyqXHtePgtodrshwXd8kfcAKRbBGUQRJsFCDOQWaz2ITqT4E09nn8WQrORijXcORHJX9bQUocMiTVvUOTjc+ehdle2l/Eh8bpF+yKhcVa/iswjbHgNZ6JCNfPlVrw0tPiwOdvlv/R0zv4paEhTEeHc4/zp/NyQHFmLgiSeWGLByktlNW2UnEnH53kB/EfXEBxPthRqs/mvtVX8Lh50Kx8wsd0OG67aREOFzBYLg7+8jFaZW/L3poVc+2g8KONF+CCpX/VilclXWPagj+sIyEteV1/GsmiDD9TlpbPyzN+hdq3ptaPFhoeZAAIwzZu90og9NEQLQsKx/Jc3/MQeVGIBpB3HkQObO165787NwvU7Zy7TqTJQ7+6PnPbwJd9fZGN0mY6+n6an3zaxsb69I7mpZ5JcwzqLBD6NnWeSR8aE/4j2ljZ+if8/qh1FzPqNyVUq8wzDOIjlc3eXNrfCzRByF1waLWL+obelJrg2ZCQtG2L/LziER2i12AUfHBn0rDYGUB+34tqjj3OGMf6NrPovcTpDLgfygE22//AIRtBA0D40tMUwNghmDnqHFZ/0AKr2TzkJLDotFUtmTmzpJOoMNPTGr/WA3sNwhYDETU54dVwk8maf8E4H02GTLTmdQmFjuELCYgYKsU7smPT2SUsRB01zemVfuELCY2XKEPjbFUSh3YCJnS6DpyeRyh4DFTC0M3jYhu3eTu1sYkJfXv6aWOwQsIEiTZR92ngALCMqVCeUOAQsImrNMKXcIWEDQHGVSuUPAAoLmNeANK3cIWEDQnEBhWrlDwAKC5gIK88odAhYQNHuLwshyh4AFBM1QJpc7BCwgCAIsIAgCLCAIWmL9H/Ni6840N8G9AAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 22.Find the integrals of the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 23.![](data:image/png;base64,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)
A.
B. ![](data:image/png;base64,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)
C.
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
We know that,
∫sec2x dx = tan x + c
∫cosec2x dx = - cot x + c
= tanx + cotx + C.
A: Answer
Question 24.![](data:image/png;base64,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)
A.
B. ![](data:image/png;base64,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)
C.
D. ![](data:image/png;base64,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)
Answer:Let x.ex = t
Differentiating both sides we get,
⇒ (ex.x + ex.1)dx = dt
⇒ ex(x + 1) = dt
Now, ![](data:image/png;base64,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)
![](data:image/png;base64,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)
= tan t + C
= tan(ex.x) + C
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
⇒
⇒
Question 2.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
⇒
⇒
Question 3.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
⇒
⇒
Question 4.
Find the integrals of the functions.
Answer:
Let I = sin3(2x+1)
⇒
⇒
Let cos (2x+1) = t
=> -2sin(2x+1)dx = dt
=> sin(2x+1)dx =
⇒
⇒
⇒
⇒
Question 5.
Find the integrals of the functions.
Answer:
Let I =
⇒
⇒
Let cosx = t
⇒ -sinx.dx = dt
⇒ I
⇒
⇒
⇒
⇒
Question 6.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
Question 7.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
Question 8.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
Question 9.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
⇒
⇒
Question 10.
Find the integrals of the functions.
Answer:
sin4x = sin2xsin2x
⇒
⇒
⇒
⇒
⇒
⇒
Now,
⇒
⇒
⇒
Question 11.
Find the integrals of the functions.
Answer:
cos42x = (cos22)2
⇒
⇒
⇒
⇒
⇒
⇒
Now,
⇒
Question 12.
Find the integrals of the functions.
Answer:
⇒
⇒
= 1- cosx
⇒
= x – sinx + C
Question 13.
Find the integrals of the functions.
Answer:
Using the identity , we have
Now, using the identity sin 2x = 2 sin x cos x, we have
= 2[cos(x) +cosα]
= 2cosx + 2 cosα
⇒
= 2[sinx + xcosα] + C
Question 14.
Find the integrals of the functions.
Answer:
⇒
⇒
Let sinx + cosx = t
⇒ (cosx-sinx)dx =dt
⇒
⇒
= -t-1 + C
⇒
⇒
Question 15.
Find the integrals of the functions.
Answer:
tan32xsec2x = tan22xtan2xsec2x
= (sec22x -1)tan2xsec2x
= sec22x.tan2xsec2x-tan2xsec2x
⇒
⇒
Now, Let sec2x = t
⇒ 2sec2xtan2x dx = dt
Thus,
⇒
⇒
Question 16.
Find the integrals of the functions.
Answer:
tan4x = tan2x.tan2x
= (sec2x-1) tan2x
= sec2x tan2x- tan2x
= sec2x tan2x- (sec2x-1)
= sec2x tan2x- sec2x+1
Now,
⇒
Now, let tanx = t
=> sec2x dx =dt
⇒
⇒
Question 17.
Find the integrals of the functions.
Answer:
⇒
⇒
= tanxsecx + cotxcosecx
⇒ Now,
= secx – cosecx + C
Question 18.
Find the integrals of the functions.
Answer:
⇒
= sec2x
Now,
= tanx + C
Question 19.
Find the integrals of the functions.
Answer:
⇒
⇒
Now,
let tanx = t
⇒ sec2x dx = dt
⇒
⇒
⇒
Question 20.
Find the integrals of the functions.
Answer:
Now,
Let 1 + sin2x = t
⇒ 2cos2x dx = dt
Thus,
⇒
⇒
⇒
= log|sinx + cosx| + C
Question 21.
Find the integrals of the functions.
Answer:
sin-1(cosx)
Let cosx = t.......(1)
Then, sinx =
Differentiating both sides of (1), we get,
⇒ (-sinx)dx = dt
⇒ dx =
⇒ dx =
⇒ Now,
⇒
Let sin-1 t = v
⇒
⇒ ∫sin-1(cosx) dx = - ∫vdv
⇒
⇒
…(1)
We know that,
sin-1x + cos-1 x =
⇒ sin-1(cosx)=
Now, substituting in eq(1), we get,
⇒
⇒
⇒
⇒
⇒
Question 22.
Find the integrals of the functions.
Answer:
⇒
⇒
⇒
Now,
⇒
⇒
Question 23.
A. B.
C. D.
Answer:
We know that,
∫sec2x dx = tan x + c
∫cosec2x dx = - cot x + c
= tanx + cotx + C.
A: Answer
Question 24.
A. B.
C. D.
Answer:
Let x.ex = t
Differentiating both sides we get,
⇒ (ex.x + ex.1)dx = dt
⇒ ex(x + 1) = dt
Now,
= tan t + C
= tan(ex.x) + C
Exercise 7.4
Question 1.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x3 = t
⇒ 3x2 dx = dt
= tan-1t + C
= tan-1(x3) + C
Question 2.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 2x= t
⇒ 2dx = dt
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 3.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 2 – x = t
⇒ -dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMUAAAAwCAYAAAChZ75aAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAQ6SURBVHja7Z27UhsxFIbVh5ICZhBV3NBh2T3VspOhzmBvqOyhIprJ8AALnRu/AB1tZlJThCfgDSgo0/kdiLXrvVqS7b1Ju/6L0/h69uh85yatTR4fHwkEAkkERoBAAAUEAiggkPZA4fs3x4yQD0LI57rQhcv9cyxSd+TOoffytSaf1Lm7BxQrKPqk//fG94/hNPsrDx67AhSWQyEiF5y1OVsCCkBRWrc2CKAAFIACUAAK01CgfAIUgKKl/Q6gABRW6Dab3R64J+Q1zCrsw6R9AQWgsKJ04g6bRns8Y0aeyYn7ejubHQAKQLG3UGRszN1zSvpvpmwMKACFdXqZtjGgqGnBfD7qXbLTp6YiXqegWGYK5vApeooOQZE9H9VM02gjFEVHsZ7rTursJ7jnfhMBS7U2pqEQQwfuDa8pJe/xPgql70OPXwe+xTy/teVT0DAagsJjzDdd4qmg0OkmDuAx7+GqLp3E5yfOZh8UosLoU/ImDpcKCOLv4/woBHmpt2QIASg2QFGkUa2jjpc5l063wGFXjib0cRz+vS7ddWtTFRS76pVUGOrT1qrJHKDQOGAy79/te5uAQqdbaKtix/C7AkV0TF33uQE4p5dPnYJCpMcBpS9Jrdh/yy++cB7PHf6ihCzEa07ZuhFkC5ndANvNueqGooxu+wDFNllCV35qokv9N4OUgSIsHcgiLhHi+pF8puvoMGKExhHOlLlOxaZWeiGLZKiqoVD1E3Vkz05AsfKNorYxnCkuzg7J4b8L3z/bxfBxpMw5dd4YccRg4+f8a3QNqAkodM6jeq4rUPz4Sn5/YT/nVeklICszrazMwYtkmqJQxM6fcvZsWZFkhjw8+QxTBRTbXnte33QW0I1c64SijO51QlFGL2ugaLJ8ii9aYpDImFEmCFLzEoJoJBc1YLZkivy9BzIn6nqmEO/fNDquq6fQQmGmpyiZKSQ9Qfi6rDHGjM6TeXp2Zm1L+aRyIl0GQfm0OQMW8dd29xS5iC8rl9Lz+iKOaQKKbbIHoNi22VZni3Ay6U6U0yeboZBBkK4bR9zv5SdN6tGlfvIkhyL8zG2PTJSdPm17O2cR3arWPbDxgPwR6yBzPlNQpEvnqDpI24fz0bkY50t1th2KhPj1Ek48F41hg8fp4CUCJL54h03z799UCq7vaC/fL9kDqROKSAedUxXRrUrdk8CkbnxNQhHoyPlRUD5nfIAuKBvPlUGxLeVTUUnfcJN53Bteq06P2nAgcNNEqi1SFRSN6txlKIJIpiiTxGbfaCSProACUHQWiqjHEBkhu8k36rmuNymzkLY4FKAAFLuXT4qz9F13RkABKBChAQWgABSAAlAACkABKAAFoAAUgAJQAApAASgABaAAFIACUAAKQAEoIICiHBT4LVlAgZ/NbAUUkGYFUOSgwP9o74/gf7QhkLaWfDACBAIoIBCt/AfyT40HCIEUzgAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 4.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 5x = t
⇒ 5dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 5.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let
= t
⇒ 2
dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 6.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x3 = t
⇒ 3x2 dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 7.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAA4CAYAAACi2pVMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAKISURBVGje7Zo/TsMwFMYfO+wU4W4coDHcAAULdQVBo06gDhXy0qEDg9utEuICbByAmQFOwAlYOEE5Q0IcaAkljePGcf7Yld7Syf7le5+fnx9Mp1MwPYwHYCFYCA2BEP62jIVAPXJ6gtsPAPijz1jLOAg3Lhq12/AeqiAwFsIiehgeKwkhKUf5f6pyt/IQhsMz5xChZ8C9x2XuuvgaAcwBkZfBbLbdaAgTD3fDr+1/5yn6JJR1PIzZJWUHxqUD9Y4uwi//Cch54yBEqSOKWkKYzQbbZB9eYZ+8psn/ewORclIDuTej2kFYHGGqFldLJTDWbxGM73hKYG/SNRKCR8gVndDdKCVip0TjIUTyDzfMS9mFGUYLDH2B0ssOxh5TDWA8HuyQQ3jiEI6Ht041IACaH3n0In5k8voA4d696vogdhz/Rk7V2au0hWAhWAgWgoVgIYghZLnZNSXSIPimhNJ0qLsKVEEI6hZFQqhlKqiE4Bt9RCbJS8ZHag/hZyNSEJZ9yEiaxbfhdEAIZCHwt4jV5ovqnkMZEDb2A0ZJB4HzVrYatPvBHwis33LAeakthE38IEkJ2KXXhW9SYMBa/WA1eHe6SD/IOsdQmh/wBm2RbxMycwyl+AFfIH9i4zIdj/t7rkvPi4KR5X1COQTRjML/d0g0Fz3eVhLCOlPUPaNQOIQ0R03ygzJmFAqDEKvrg3Ug0vxAZkZBZc9CNYT4tThYk+OB8G6gqBzOO8uwKQR/pd0WyBZJumYUtBnjqhpERZLOGQWdEP6oQVQk6ZxR0HpExtWQpIIyZhSyRNY5hqwQlia5FoLGGYUsITPHIH1hyntpqmLIQPCb0FTNXTY3EUDuzpKFYCE0K74AX1f1wRVLiwcAAAAASUVORK5CYII=)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUQAAAA3CAYAAAB0KzMdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAdGSURBVHja7Z0/bttIFMZHfbZfLzzqnD6iU24XyISTLZOFRKiK14VhENgkgAtjQbtzkRxgXa23yW6RC2x8gfgENuCcQD4DvRpKlEYiOaSo+Ut+xdcogW3MT+/je2+G88j5+TmBIAiCzgkWAYIgCIYIQRAEQ4QgCIIhQhAEtdIQw8Df3/O6l4R430dRtAXYECQhlk5OfoIhOqbjPn1PKbkjhDzCECFoAzP06btul9zOYwmG6K6GHrmCIUKQxFiCIcIQIQiGCEOUoij0n1FCHqYp90Tb/nUYDXY8Qr6nn3nB2SsYYrM04z42wR2CIVqdIV5cHD7xt8k1HwRngfeKEPrgB+E+MsRmSsB9rJI7BEO0vmSOotHWNDugD/3R6M0u3f1HtVHBEC3IFKfc73Vyh2CI1hvicvk8yQzD6Fk1CLOSSyDaP34PQ7S+fK7MHYIhWmWI7Avco+SGLcAgjHbkLiz9JDIxZIjyTEgVQ9u5gx8MUaohLjIzuU/0JFPwhp8Cn0Y6muptNsQZw9iGrEw3d/CDIUozxKTn0927PLy4eCI1KCY/N+0fLZrtamG31RBVMZTJ/cXRaQ/GZz8/GKICGEkgUPovb36LvpKakiD5nbvkC/v5betb2RJQZdxfH50+hQHab4h8LDX9QZZf3pDejcysarUEz5xNlFxGTY92rGy+eMMrVYvI3vVk/R5b+mMqGMoo+7izibGNZxFt4WgLPy6WYl2xZJpfAQx6h93AamLvTZftdpsJKDCswTG2gSP41TBDn77j+H2AIRr/ApMHGCI4gp9xfmNkiAgkMIQhgp86QyQPOBrhuiGCoduGCH6bGOKkdO7AELUt/GBnemiWPBLauwlCfz8NJJOXWYBhbY5xAce8yynuVXMEv+r8PEq+pfwGx/2XqSHm8Ts6ff10id8g+gWGKDmL4M0x/WzTyywWu7P1XlkEQ4kcKfnKB4+OyynAb/3ymDPH+abKKj+WNab8+oPjl8gQN9Tc6FaOHaTHfHiDMnGZBRgq4zi9nCIIftXBEfwq8GNGN+HHl8bpESF+lzmH32fR4XLAkNBjKvtc9+tXYGiWY+CRv5Dh68sOq35e5Q2pgl+Wv8NV5eaZpikvg1j9ooqa8SYuNSjbpawSrOBYyPED+BlRJhNc7QGKdpkDj35Ms0fRhsvaMNqsvJKqNLOocamBnB4iGCrjmNOM12mI4JctjUszRC/4OOMXi/hlYUxq7h6hNzJhNCGrWOoLbvvX/HumeYFk4jILlQxd5Vi0PnOOJyc/5HFMs4gMx6RJr/ZyCkUx6GpW2Sngd1/Ab8xngTN+Sd+wCj8Y4prBNH9VzxteMVNki8xm1s6P2uz6X8Kz8EeTlxrAEMUMOY5xwnESVCKOfPDo4AhDFBsi0/xVvd7w75Sfv9v9k+d3GB1uFfAbF/HL3cHZ63qXMnfSRF9MFxX2vYP5wrPzaeGLn1mJ89wPfmcmafpSAxUMG8xxymXGsUu6tynHxeaIXo6KYjAWGYyT/Pznb6vyY6aYy2+lfM6UEd5odND3+n/IvHqoaYFkq1QyTIMK66yBXxD8piAG4yaZoSotPZVU9LnKShdIbmahqlcJhpr4TXtcYwX8YIjrGKKyX1DTEPm3PTAoyoIvSk1D5DjGbbhx2VJ2tcpl7k2P1rCzNpBYfyd9SiY9uZWdXcgNQwRHdw2RZ5f041Z2dWGIhkotm24QbnNQgaPThtiRwg5zmfWXyxkYyTGE3lcEklvZITg2yBCTDR/vv6azc8MQJ08nrx8e4MvtuCGCozPlclvZOWGIge+/Vdl3YsNp2KFcbN6oNUSVHMFQrSFqjUGDZbn1gcTeKFB5iJn9fErJHXaz3eXIfna3S27BUE25rDoG2VsnS/xgiAKzSi+AjEZb/X74RtXf2tah9lWDSgZHFpgqOYKhfEPUxS7JQpM3SxpqiJuWy4tZzqnUXoyAYFLzUMve3KOOIxjKNcTsvY5qY7BVhmjDrBEE02aGKJgzAob2muG8f2hyTkwrDFGUPeT926azRhBMSh9enSocBQzHYGhXFpj3uak5MY02xCpXLJXeRWdg1giCSQ7HpTkVYGg6+yu8JqvIKE3MiWm8IRaVxlWyR9mzRrL9xvVumG6xIcZ5pVXe/1HNkONY+6bwFhpiR8RP1D9cZ87IeoZWn19jeoir5ldlQ8XErBFkF+XZYtWHGhjaXTZXOX844xfrmBPT6AyxLJjKDLHurBEEk5YSrFM5ywdDa/mVGaLuOTGtMsS8MrowkAzOGkEwrR1Uj+swVDlnBAxrldEdAb/POufEtNIQ0wAqCqTp4hfPGhmE0Y6JRZjOYyBf2N/Q9klnfJM+r39YxlD1vJgqDE0Htg2mWGSIKT/dc2Jc4acqmB6Ln+CLA56Zs4kGSq90JOWSvOEVskQhQ2PzYgQMYzDM7D538rMwN/iZuOFbqyFCbgUV1qIZrQ/IkCGKymXIvaDCOrhdNmMtLDBECIIgGCIEQZDj+h8Jq0QfvS3OkAAAAABJRU5ErkJggg==)
For
,
Let x2 -1 = t
⇒ 2x dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 8.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x3 = t
⇒ 3x2 dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 9.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let tanx = t
⇒ sec2xdx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 10.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAA4CAYAAAD3u3YSAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAANwSURBVHja7Zu/ThsxHMfNTvYS4Wx9gMRk7VQdFmJtRXLKBGSIIi8MN3S4ZItU9QWYYOzQuVLhBcoTdOEJ4BmSni9/dBfixPY5l7vwRfpKJ5Sg7/lj//7YhgyHQwKVSxgEQIMADXo/0KKfAylAK4mEz89OWe2WEPbcCcMjQCu4+h69qdXIv2iVTQCtZGozcg9ogAZogAZogAZogAZogAZogAZogAZolgqCboWfkF8S2ufet8Y+7kHu1csMfHYeQRqnxPw7QIMADQI0QIMADQI0QIPKCm1+IQYqljZBG0PFk/PwiJWQ7ypzBW0CbU/bhoZQlkNodAltjKquRCW/agnr5kFAyBnabOCNoI1G3UN+TB6ny589d4KgChD5QpuYQhMeu+IirMvn+IT5mD92R6NDwMgXmnU+CwWvU9J42tdrAYWFluX7Ydg5apDGA6DlBM0mn61aacwTV1t/yQIXPjbecs1ny/I5v9x2Puu3mi1KyOvUL32lrP2jGwSVIgCz9bazfCb/l4z5g3Pb2anzuZUXfaTvLRU/Jqsli7fc85l8MQmMev0b+RwEnarnia+u82DcWlD6s+mLi0Xl6vOzaGa/SO+2E8ZFfs7qzTm0VfE5+Tufkbv07KIv8xbA5eDIfMlb4SfFDFcOzCb/LqDZessETVWE9HpfGieU/iasfZ/sy+IZRPmDi5CUteKUq1x1+ziLfxeV8Dpv2tCURwMr8lk6RtNXebvXZyxsifDjrsLQKsmGXobm9TnG3L8LaCpvG6EtnedMTPOZ8JsXcUVEG08mYU+nJJ7nwHhwgqCqc/b0tplnf9cNrK5/l750va2DNklVM6uOu9dAW+wtOqrQ3ubAhS+j69/z5L9pIun6d+XLxNs6aOPk8zIgnaZaNzbnGR5lbtKtGG38ZwmPJt60CpHl1bapqZbmOWPfZYhxXVbbDs68xdDJ17b+baGZeDOBllptqqZ6UdJzfikG4kMcYhJV2K6g9T12zbz+dTr/dCunNXab/BtZ/dtAi1eYhjerkn8G7kCVz+JwEr2gbBCXj12EaNUZ88NdQJuGOcX9iwQQF/7NJ5Oet0x92jxMKqFFTXKyw5cltOxv4v00h1tGcnAYYX82Dc5sUJR3L5Khz4V/XV+m3rJCG7vYJIYc7HGabl3hEk/5oAFY2aBBgAYB2vvRf4gRfMgCqQiMAAAAAElFTkSuQmCC)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUAAAABBCAYAAACgu327AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAlvSURBVHja7V3LjtRGFK3ZQ/ZEuHeQNV0zy2SFjANkOSQ91qyAXoxalsKM1ItRYtjNAj4grCCbgBR+IPADM19AJPgBml9Id7r8Gre7qlx+lcv2WRwhmoG+lI9P3VfdIs+ePSMAAABDBBYBAAAIIAAAAAQQAAAAAjiA/zwhOwwgAgBuQgAHhdnEvneHjl4SQj8f+v41kAEwBZ7r3AU3IYDNiZ9tHY9G5ON6h12BZIBR4udYT8BNCKAWHFDyGiQDwE0IIEgGMgDgJgQQJAMAcBMCCJIBALgJAQTJAADcHJgADqEPCSQzjIzofQM3TRBA33NujS1ywR7AxPNvgGRA0xgK58DNDghguPhkSYi1cDz/FkgG6HkW/eccuGm4APr+4TU6uvNyenZ2BSQDtHh/A+IcuAkBNALz+fSqs0veMZLdPjodDy33ZNL/FwIIbrbF420yes4ti4wv+rzzPHXp/TDcSoG6r4ZCGnYOmuXbLHt2bIQADoBz1bh58Bpitw12ZroqjwVktP5FHqanpHGsJ9GLtTJLAME5oDSPTyCAQEHBIV8hgEAPeLyABwhAAAEIYH0CSL5S9+l9LHJ/EDcZM2QFMP1ncVI5+3sdggzOASV4HAhglsOqPAYZB4DTo/2bYZMxWRKLnk9m9r1YAGMShfPn1rjufPD8yQ1KyKfos6WMCzziicgIAQSq8pha5Dzk8fgi4vEixeMvaR4fna5/PofHIGPvSXN7nPb2fG8tbiGJkiLI2dn0imOR9+wzOvF/Yp+F1Uhr4bjeXdm/71LyaqtqyYEsTAHngKLhbobHJzwes4034vEXEY9Bxh4jIMR18iHbRhG1WmxUgYNevGC3tL7arvvzrrX7l662FHAOyOUxE7Y1j9PRRNwylK4Cc3k8n38rjGCKkFE13AHaA+9ZZr2vvM8ZeXQWJPIEEM8VPOYVO/I+ZzxmjeTSnCKfjPyKnEqoA7QLnqeXFRZZFfiAWi+yu6pqUrpaDlBcBcZzHSS2PL04PZMngGFqxnoe81jGv8JkrFq5AfTsmqJQN9cDpAcvXMfy0/lAPTlAcA7gCxUv1M31AKn7POLxMs4HqgngOoYeE+uiZjKugObBe5ZBPuS682E6n1/lCGCyO87nh9/Geb/LZHJ+CFFLCAzOAZfYKcjjRZrH7GeL8FgnGeHWawx/YyRHhujBa0YedtCe3Tkb5vrWn+/++PfUn15zLOttmiRx9ZgdyN8/Or3ZYQEENzoa+nJ5PD74c386/SYcGDH645LHzjsJjxchj+ffSQWQfTlTzTsj+rLOCiDPOwH0wbPpo6jXb0ks573n3f5+REYf9xz3VzaB5TKMDWfxpXoDE2I2VaFtknPgXc947Ow9THjJ+lUlPGYimOoNFPI462Z+pq772Kb2b3WNJopi+1WFv4sx6T1FU5zrswB2/Z0wzf7tXpuaJ/KWJWKqqXEZDIaU9PIAHe/vamAKdBz+9nO9uvlOmGi/DsUvRUQWtsUvRTAdlyVAMTATGHDahYWA8TsRhHsdeye49qeKGr0VwMqhEgZmAhDAXr0Tof30vG0vUEe8X10Agyrh+D0EENDJO6MFJMif0n86K4CG2K8j/K3FA6S290jTi2Nsktl0+0zy/obgAep4J5q0f8/xHrbOlS4Q0XWch03nOmaTvUnUU7RijZPsRETb+Yku2dcVAfRs+4HJ9w7Hwpa3wel4J8qsm6n2tymAlSpxM9s6LtODVsRD4l5EE80Ua+ohmW5fDwRwi3cupX4Xpk6z5802OBFHyr4TpR2Qguv29JDeM8n+VgWwikCsF+okPubCjmrZtvdANb+gmjMMS/PW2z3X+yXZ7VznbjwktIkHZbp9fRBA3ktnyhUA2ZQG1+NyrCdZe6N34rjMO1HFARGtm4r96T9vw/7WBJCXiCYFRlZvH7JX7xUrIjDMZXcm/g8Cr2tDYIrY34Z9AF8ATayYsk2MHUkUXX4eFgms8/SxrirvRNlwPKjUcuzbsJ9TyTXB/rYFcCMPU3X0elMelmznS5OzTvubsA8QC2DQR6rhbl3VTZB5R6MR+RjyRvwMA8Go0e6ihTPRum3ZL2hlie03uWBX2X0Xjpnh5GGqjF7XLYDs4Wdd/7rsb8o+YDvy0DVtuswzDQRGIoAht+o5MVHUvnjDl61bYr/AvjrtN0oAI5ItZdU20eeckdVvqnox2dCU5RaCh71e+DKtIzLXv4z9Ou2DAG5yMvSUxROu20hrqApgIt4Kcxnrti9v3VQEMBHRGuw3TQCX8a+iGV6yAkjdo9cFQzm3RyFR91XevxUXHWR2FbVft30QwMvIQyYybac1cgUw3mxrCIOL2pcnbkoCmLLf1DC4DsItBcWOlXyBg9HrK9XR67pCYHYGWYX0VezXYd+QBXBjs2CXQknahdpMa+QJoIr9Tdi38b2SXtM8AUzW1oAzv40JYGrX3RGFIdydt+DodR0Cwyv5cyfUVrS/afsggBseyOc8ASlzI14daQ1lASxR7Kpin+q6KQugwXnAuki34QXKGqCj0etvmhy9XkZgZjZ9TO3Z403STK9mB3XWYX+T9kEAtwsgKiFkkZvEiqU1xN+tLoDFU0VV7FNdN3UB1HO1QmsCmPUCRd5fMMZaw+j1EgnfE+EdBSkS1GV/uYR0vn0DETipV1VWAFNpjaWutEaTAljFvvS6KXmwEMDNgohIAHWNXi8yaSISF+EdBWl76rK/iH3JXQgK9g1B+PLSK1wBVMihZW4S05LWMFwAF7XlAIcggOncH+5iABoQwHQIJ+o82CmTA6zjRrxmBbB6w3shARTcwoYcYAGS4qUFmhDB9EYr2ICXWwIiEcC20hrhrWbkHfsO9t08QW+1CpxTvS1sf5+rwDySAoAGb3BHFP5upi1yjptpTmtwp/vwihGxB1tTH2CRAaTJunE8NzbtZW3zf4r297sPEABaEsEVp/90xRebehrudUPXMT6xSIfXS1a0f2FynhovE9AbL5AngLEXYvJxLLkI0U9ttDnVsW6J/X07CwwAJnqB0u6DDrYL6ZpiIw2DK4Svsf29nAYDAKZ5gcIBHIbcQFbcA7PO2wzdq6ybCfZDAIHBeIHxhCLRz/EmLJsMUyZY8yY7d8l+CCAwFC8wt/fUpdbzLjSOBxcLUfd3U+wpum6m2Q8BBAbhBSp5NB25Fc40uzzH2Ve9Fc6E6y4hgMDgvECsBQABBAYrglgHAAIIAAAAAQQAAIAAAgAAcPE/s2AXUcTh1BQAAAAASUVORK5CYII=)
Let x+1 = t
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 11.Integrate the functions.
![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
Let 3x+1= t
⇒ 3dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 12.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAA4CAYAAAAYeR0sAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAN5SURBVHja7ZtNbtpAGIaHfbJPogy7HACG3KByR222rUIsViQsEJpFU4lFF4YdanuBdpUcoNtWKrlAc4IuwgngDHY9A6YG7DA2HsdGL9IrOQjnG/vx9zczJsPhkEDlEW4CgEEABu03MP9TkQKwEqjXtN6+ZtXvhLBJy3GOAazIsCx6W62Sv753eQBWIl0xcg9gAAZgAAZgAAZgAAZgAAZgAAZgAAZgEer3O4e8QX5IYK+6n+r7Nqe4V7AGNrvwAbkrYvYdgEEABgEYgEEABgEYgEFFBRZsXoGKo23AXKhYyjwkwgvy866sgHmQGZkGhhBmOBxmCcxFBVeSsj7OdaFk+T8XYAtjAJZCo1HngFMynoc/Nmn1+yd5APMALJ2Exa65cGry2Gbkjpzyh85odJAHMOSvHeUIXqOk/qizpQH5qwjAnNZxndTHRoFF5a+kTWARknhRPIxZ4tpoDlvPX3O3JrPoJpDOgnhtCpR8L6xB6S+VxCkf6+SDosjmvK073szyl3w3K6YB9Ai7ujd1sWqX1Cl58B+KKWX2VyEGR2XyLnnfmD24MF7Wh71LlaiMfWkK52z9d3KPYJIBJYPVOmGETPyy+CnKdtF7MAmLWr2P8lhei2WJ97kAc0TzLOqGJUmmqfqYuWdphduo3GYy322zp0r5lUhEp1rXYbJhVvsEDYXDxR5Ez39Cb7cVG93uu7rKb6GxyD7Iz7lTE/nOpL2tYHbpv0yFw//exSbc5m1GyZ/FUzpjVu8mAmzwFM/kbmCbMcdUCDVt79nSOHaKX8O7dMJh2nUh+b9V7qL1x6YQtQDiIswor9uYWbDPL1UV65+zLfTssl6Vxt6uwLyVCi9qmTqjcLgZx6O1DiBoITa+D0BGvAix9EqNKaC040prb1dgbvg4pjn2XiocPgcssBtXiMxbj/zeajFhT7ffqsQ1zLtOtaSdylGeFOHBcTdJniNbDwna1IO0Ya/R+Jy1PR1gK16mU3CYrA5Xw9bmsoTysJDtZRnNeVsMxJEKUwbHZtqe7iDcYCAvHQ7XvOxJ5Yh+/zBoRMP9jPrbv1nC5m+C7xRQ/xwhmjXGbCfzEGjYXtKpqIpOOGSE/c4jT6jE3qh+WxYBtPEzXD4HAM9tcRn2ftkPyWmsrPsvwekH0/aSAHOxYFmAKa2k01FYsCwXMMAqEzAIwCAA22/9A6+VOE5Vkbp9AAAAAElFTkSuQmCC)
Answer:![](data:image/png;base64,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)
Let x+3= t
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 13.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 14.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 15.Integrate the functions.
![](data:image/png;base64,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)
Answer:(x - 1)(x - b) can be written as x2 – (a+b)x + ab.
Then, x2 – (a+b)x + ab = x2 – (a+b)x + ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANwAAAA/CAYAAACLiqatAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAh5SURBVHja7Z07bxw3EIApFW78qGwEflBVnDjufNQhVRwVxonyo0hxVu42hxSyrxCURSwZ2MKAV+pUSO7tyk4T2T8hcp8ovyBA7DKNpL9gKUfuQ+vT7h7J43K5t1MMYAvS7d4MP3JmOByijY0NBAICYkZACSAgABwICAAHMmnGR2hqINNMQB9mdAhKq6l4Xv88xWh3MFA+IUQ+9jzvCuileB2C4moqLm0uUde/xf7tEPQaXaPv+5ub50A3xeoQFAeCfJfewqjxd8/3L4M+itWhTl92OkvAIOXFFSkydWqw+L3LBJE/TAKX9h4263MkcII61EM3fxj6GPiyw4L3o2UXxJSrg1fTbYGOcGtlLW12blJ3yeQAdluthx3Xv16FlYu03EejoBPVoTbgGqixWyWXJFwFKjPL6njvdYfcHwaOfZZD6ZKp+I0/jxC/SpPweo/cw6S7naV3GR3WEjg+wzr0LqVuu2qJgicOXaCOe1cFumHg2GestPAa6a3fM+Xmsedh6q5a5HYLfWfmNQx093T492MdOuv3RXRYO+B4Knd25mXTcRcti7eEBzsP0PHCTt/zzqsCFw6Up+Egmva83pVWy31Y5Hd9tnynYUNyho2BDiWrGKHDCBSxsAnv3Vl+1hiCTUqHtQKOKXoB4x1b3BkVwyehm8Wzv8vsnyWB42lsw7F2l6A3iDivy9Z7+N2PBnIso3f+d6T7Jvp/R0GHtQGOzUZdgrcj98kGUTX85ysdfSu60qXFcCaTDyoTS5Gurazemf7GLRKoDXAmYwcZ91DF8CmxxZrtwAXfEx/a4l2o6D2eNDr+AwAu13XrXRm4Xzsm3k9WF+MCt7nZP8fc5GRsYSNw3J1kq0OOXlL2D6dMADf03Kn8OA59SLqVAFzW6iYx0MYx/DjAiRo+1dURGARlAccmBXoNvc8rfWLxLHP5P9szbHRfyCaGZIFrdlY6DsFbIs8U+R61B44rCeO3oq4MN3wDvwhjK2nDqwInY3jVZ5YFXFwYkTNQoxUw2gwPN++PWQawSOBmyPyroWceoUb3t7QJLwZujDhu4oGLEwuCM9Kw4SPDiA5UVeCyDC+TgBkVW5QGXBj7ZK3CwaSIdhGmu8xObLAHWwjZfzOifG2kd5LlygeJrPRY8wQ49Vh04oGTcSd1GN7z2leZLtqed7Uow6u6lbYCl9Rlv9++4NDmk8HvHzC9ZP3N6W2NdMlKlGXpPchEpsfUAJzgiiWbkNBg+ONTP8vYf1IxvOpKXjpwQjEc3m9S51fXvfOdCKQ6kiYAnMb4bX6GvJJ5r3ENrytLKQ2cwHNtjeHSkhGiq2IxwOGDfJcyP9taW+Bk30uH4XUB53fIA5mZVCQ5ZGuWMtJxMkGSdOWL2B6I9Z6Ie4PiiEEMH4YUkKVUmVln5l+JKidh+DVVwysDJ2H4bPcZb9sI3Inrnb4yhHo/YAO53e9fYF5GmLHliSNWaK77KI/rNBf557NnLntfszg73JzPLM+KV2rYh9OTocwx/LGo4WV1kWP4A9k4wWbgQlctc8Vm7QoGut/niQ7ibLl+53rQL2Tg2jvuj0W8Ezt5QTD6K4qzZ2bpyzz76ihPA+DkDL8oogvZ09Oh4fdEDa+aICq1ljKs0hinLKpsCWspP4wzzicbuJ9v/HDmzDdMQV9U1cgyMncJ/Xlpbn3VRuBit7KgJIgJ0XHaAYCrEXAsEVMmcIFLRvaq2JKP1eOy83DjFl8DcDUCTmVPUrdEpxuq1t5C12kTo8ClVV4UWR0OwNkHXOBa4i1bzsWJrsyEOM91fFYSBuXaNBHgwgzPfliFccxS3iwhwY87BD870n04VCVpUmUZBZQtwAUrHW1XpWuXzo5mnwe0irVpoitcXKsY7jsxeMMN3gPqPFkoJGYA4KwErq5iPIaLD/EhfNhynEXel2O0K6q0+gJw+oAbtzofpMSkSbzBLFi6pLr6ygAnOJhKk7KBG8cDsl23Ju1mLIY7bXx+uvcorddfGS6lyGAqU6rsUtquW5N2MxrDRcLrE4mz5VD8fLiOEGI4iOHApdToUoYNfXjcdpJEwYciTXAAOAAOgJMALrjADr9LwhVX4yPysb387Cud7iUAB8DVGrgTtzU4ApHYm4tdVp17cQAcAAdZSoMClSYA3IQCN3fzIrr435zv36wzcCYbmaoA99OX6N1Z8st2LQe6JXuEAJxG2FY6zU4Qj7JSNXxYZCNTAE5cojyBDas7AKfrWbxELW4e+ym6pIP3vzAEHQB3Wk4a/6i3kwfgLAMu6u+fPBHOTnFHLfZMGRqAS58ITdsBgCsYOJYNpR3/9vDPZVvd6QAO3/eXALhA4j3fHnkEwJkAzv32+7NnbvxTVpYyaAY0Xg8MAE49pub3AQ4gMz3x1Re4krcrWBre1J10In0p6wQcdyWJs1WGp1Fb4FQ6L+uSIDNG9kw9W2RyGQD3tg7AJcsHJxQ4m+8WyO/VWIzBzd8lbvPdAmW48km4ADjDyjc5yFjs4LbII9N3ifNtiREt3OoAHJ94Gt0XyQKEcMsm6jIwDcAVbQDS3TYFW1p3JxMVDiJlW3UALrxbb/hY2VHUNyevlTkApzOOK7gXYgAbeUxaK4+Tsyu79qroONL2G1DLFnApS5j1ihxo4cr2NO5INixjduvV4U4CcACcObcyer+CVrkMN+bkyFGBhg7PGArdYV5b4HrkXtF2AODSVrlBLDdpXaVkOgLXFTibpDbAMeEdfyt8e8uw8L0+vLAjesAWgAPgjCdQ2P4Ya/FQ9ZWOwSbS0xOAA+BKh46tdOySvypCx7tV801u8ZUNgJtQ4Nqed1W1ialpYcdnKHXbVet3wt97RFv4rB6jZV9XBaIROILQv+lZunI3GusoeVlTU8XUIAUCBwICAsCBgABwICB1lv8BPIWVWHth+5EAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
Let x = ![](data:image/png;base64,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)
⇒ dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 16.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 4x + 1 = ![](data:image/png;base64,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)
⇒ 4x + 1 = A(4x + 1) + B
⇒ 4x + 1 = 4Ax+ A+ B
Now, equating the coefficients of x and constant term on both sides, we get,
4A = 4
⇒ A = 1
A + B = 1
⇒ B = 0
Let 2x2 + x – 3 =t
⇒ (4x + 1) dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
2![](data:image/png;base64,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)
Question 17.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x + 2 = ![](data:image/png;base64,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)
⇒ x + 2 = A(2x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 1
⇒ A = ![](data:image/png;base64,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)
B = 2
⇒ x + 2 =
(2x) + 2
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
Let x2 - 1 = t
⇒ (2x)dx = dt
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
And ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 18.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 5x - 2 = ![](data:image/png;base64,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)
⇒ 5x - 2 = A(2 + 6x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
6A = 5
⇒ A = ![](data:image/png;base64,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)
2A + B = -2
⇒ B = ![](data:image/png;base64,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)
⇒ 5x - 2 =
(2 + 6x) + ![](data:image/png;base64,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)
⇒ 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==)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
Let 1+2x+3x2 = t
⇒ (2 + 6x)dx = dt
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAAAxCAYAAADa4RzkAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAnJSURBVHja7V07c9tGED5KreW0fvDQOW4tHtXFnQeERnI6RiIxbKyYk+FwMLGkDAsnId2pUFInduFHk4ySSZdkIslVGkn5AR7H8g+I5J+gR3A4HAAdAfAAgQBIbrFjmYTE493ud7vf7d6iJ0+eIBAQkMkVmAQQEAABmAQQEAABEJBxU2yECqZM0X9hPiYMBDyLP5W2Elz87K0pULDsdKC1pC6WMDrAansN5mSCQIAufrtG6hihD+bP5wjhD7hU/77abF4d9mdvmYZPFa+M8Z/mZ58iXNlubmxcASVLX1oaXrXWwNQBEQTAMxhzEOjWyH178b1yjorq62anMxMBTCLt4s1m9WqliHZN0DnCRN80jN41UK6MdcHQZulmIIJAvVTqNbrd6zBHYwgCGxvNK/MY/zynG0v8tUe6Nm8qwhEFAqL3FqWUp9u4XkKlHVlF6XSqNwlC7xEi72pG9xYoVX5B4HHrnhkhlA4ABMYUBOiia43eXfH1nk4WhwUCnU5zRi2i16YHcKwZ3dkwz0LkCrLiLcacC3DmVAQB11sj76uGUYzq7QEIjLC0VbxmLvyhLPpHAQE7/LDiziCj7q1pd6g3UkDozApNsLZjdGu3TO/hHeMt0Clp9BZAGS8nnVb1NsFo35zPE4TJXq2tLnAQoF5iBaNtZw2sMBEfhQE3gMAYSZ2gl1gzVqU9CkkQoIql2TuLpmsrpgLuUeUqmF4BUdtNLxCwUAVtUwWcrX3zKX2PAYipiPqjeVDEywlz8wvHWGutMq/QBFkGCBeIQaoLdL0gHEgJBPiumL1ykP2wRd+6uINP0RjfBIHdaqdz08+N94KFxQVgsl8zjFlu7DpBL2zlW/d5/h09sVB1fbmMyz+BMl5elxwwJvWXfmEggEBGIECNz7S+f+iEZ0WW0XidEoWDXD5TMZ77nCic9b1G6s8HEU8eYz/0UzY7NDimQHCv9bgECiitSwdBuhS4Dj6vAwikCAJssrOLu6i7bajk8zixtmw44FGydfE95g3gD37fvU7wdxRksNpaB0JQWpdOgnTJIX5r3fuTDAJRvG7x2cQHY+2ESuVpVokyVsKQitdEHkB2kqRBgO/4pfor8b0gMtIKT4i+qWv4W0pScX4AjD2+LvUaZIGBqhB+TR4InMnqkvjsWIEAAwDStIk5J563jocU8lSK8Y9wOsB2fPKe8gfeMSyX0CtE9BcXw5PGDc4DWHEsRjt2WEBypEi5yreX0SUHjIvq62qzc/UiH0RB4IuvOJ/jgECncyON75gmL5YvELAQOP2EDNsDWLePgPpFMMokQMAh+4raLk1NpgvOxnDRdaX8hIbxFjV4PvmmkhKW3myCSKtzO2vDy2O+vawuOWnCpeVX5jp8REFfKys/2unjZ6g8/ysFEh6m0XXQNe3BMDcqemRZIcqztGwhhyCA36bNBRhuvrivyPIDzLDJX7ILZ+3qZeUHFreiU0Up/y4SWDb56MS1tqt6FGd8w5KwfPtsQUBOlwxtbkVB6D+WJ1DZNox7dxWkvJnT9C+5sVNi1noGk71h6qe9OfzL8hLSCT/8QCAIFMYWBECSWrt+pn0UQCCPkiYH4QcCOiFdv8+WBoG48SGAAIBA0iAwqsepWYJAWJ2ENAgwhls+515UpKi/B5IZF+Cbb99/L0P6NQ+jrktBICDM4dSATViKXPQatlsnUfKtk5AGAR5jR41VAQRGR8Ly7TlvEbfmQczEDJFCHnUpifH7gQCd8zLGf3AOCeHSgZcwtp7pNGdqGlnlvJFC1KeU8DR/ng66rIYbtkydREqcAIBA3kUm3/4yNQ8uGRpM1lLhn583XUpi/CIIBMz5Hp9fjxe+zitTvanoYZfViIYdFooACIBEyrfPsuZhnMIBZ86L2q7XiO3veMzzF5y8B8/aOPMgZEUCCIAkTgAGvZ5VzcM4gQD/LiLwColjJef/xcouvw3LTXwKJmxzCAL+pwNIPs4CSVj8dnzRuMJOB9yaB5qBN5gQTI4TCD5pGsbcDIsTsOf8TAQB9zl3PWgqNAVdUmvXKQ/QYklwp2FgOEogcAqSjVwAAZZvfy6Tb+/sRBFrHpLjBEJB4CTpuRkWJ+C4/T73XbLn3Nup6NzqBG8qCnrDk8y81+YNDQQG5QXI5g2wtFt8AHkC2bHZA4F6YL49rXBkLLRY88CIwnRqHkZdl5ghlqxY33X7XZKVnwRYx3lY2+FcgVUAx6pMp8PutJACAZ86iUAQGJQXwN83EWkZQCBfwmoTLAU7KSBy6C1oChIh3/6qT779L81u83olw5oHBlZ4fxR1yT2r50Z/XrA9sFPr/J7N3TSzK/cIzwsWfWJ5ERszMiAQVicRCAKD8gJk8gbYzTwmsklW7IEkIzRvniuRtfgCAx32e04Ng5Vvr33izbcPqXk4GXbNwyjrklOj4JknHjbQ9+xjwcBaE3oXhjjPzt8JIAdFww6rkxgaJ8Cv2yK6/lAj2tfQeCNL5n+0r9Xm4cok6pJVzamSh37ej6HPLc1pxooMCEThDxIbPM9Ugltc82BAZHuUQWCSdck6RaCenE+znMet6se1Wu9ObkEgKtqlceFCln0JZV3epMdGPYGg3QIk/8K4GnxE1PZDN1WY1nXUbmma/kDWsHMNAqxfoLpAL1wYZoVVln0JZYQy8fyacuRzTXnc76xr2gqEYu58jCTHY7r97vGgqR+K8ibqEWGuQYASjPQLxrlwIYrnkFRfwqg7u/xuzcg3KzfcPn8PSwuVAj0Vr3GiDu4unKy+gyMXDlgLFLHWOsq1X0n1JYwai8s2LWlojar4ml8uv6xYHZFVvE6Tf6j7SHsnqKrx2SQDwKT1HQQQ8NlpZfoSJlkvH7WRaR8IYLTjzT6LMrb+7LbJJmcnse+gvf6FOM+OJQgEifcq8JB6+cM4PQLjjo8uhpWAQ/RNB6ygf2Fsgb6DMQBkkkBA7EuYZI/AOOOjOxYjL/Fbdam1CP0Ls9MvAIEcLlLcHoHhMWJ/X0KhXn5Jtl5+wPimB43P/Vyn7Rn0LwQQABAQ3o/VI9BPBvUldC92kK+XD6gyizy+nmFcqxG8GXRaAv0LAQQgHEgg5pbpS+jWy7dj9Qi8bLgC/QsBBAAEhmBksn0J/erl0wYBdnLh1pSHjQ2AAEAAQEAaAAb3JUyqR2CU8Ykp0w7p56kpT3JsEw0CKfUdBBCI6J5btesE/UYXidWqb00lbGRSfQm9PQI9O2+sevmILc2PFVJ5Zv/9KZpGjTH+e9T6F+ZZ0uw7CCAQ1e11LlaIRu5F6REo25fQJR8v3yNQdnxuhRwnFfERdfcNo3dN2Mly378wz5JW30EAARAQEAABEBAQAAEQEJARlv8B1s0Z3Dp1PmQAAAAASUVORK5CYII=)
= log|1+2x+3x2| …(1)
And ![](data:image/png;base64,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)
1+2x+3x2 = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHwAAAA4CAYAAAA/15zEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWISURBVHja7Zwxb9tGFMevGbwkGYMmRp6ADC2SMTob3doMAX1xnKGDm0qE0MGNB0MgCicABwOhvHmwsydZkql2gX6BOmOBIP0ARQokWzfrK7gu350kS9SRIkXe6U6+4QGGB5Hvfrz3/u/xHcnu7i5xdnHMLYID7swBN+2mCfnCwbsAwBF04LNVxoL1zb29Kw6gML4mfrCaZyNY41QYbl5lS7WXy37w2EEetyhgdwEeHG6G4VXrgSPsBwCHLIjuOrjZ0Jdg6ddWGC5aCxzDVJPCAfU7a9bmzdiHpKnd6ewobacbv1htD54CC7Zt3nntxnIDCOnGoM8IgS7Umy8mhd5SOZ3BNnjtp9YBD8PWYhyiDltRdMPaMNugj2LQ/yXsjNxk71QJz729zSuYAu9v7dStAs53d8qTaoP1Fz4Wmj8OK+p4t58gdJVpquPTNUKbb60BjovFAI5sFmqYT1kj+lYKQzHwKGrdqJP6cTI6Gl5mxOJjDuttjFyE0E+qU5VPyRvaiB5ZAdz2cJ5lTUre6hCisrBu9KKoCHk6SqMs29m6XwdCP+gQorIoaWz+XqnRV1UvCu/WATkWSpl+zmpQqKk69DaQZHnczPydIjjK16fLG/3FxvymsjSSRZbAoz/rbCDJhK+xwGlt5ZVKGDzckfpfOkIrwpY1kHSkFexSmg9cg0LnDxWhf6gGLmDTJ9RrP4n/vtTXDxjeVaStwsB1CJpJfWUtwONrLLNgQ8POfiZaqhKTNEZUi9/Rm2t4D1do7TUXNIqePFxoCuSDEE5wgk++buDoq8/Yhur8jT3t+FqnktYqNx35PBU43lytRj4OFGwB4HkjgthV/i+40CgofAbPZR2n6Kfb3y8s3MHGxJeq8mn/mkWjmW3TNveukffX7nW2U0M6PhFFgOdV1Ai4xVrrYyryJnmXDG2qgPdDLHjtZyKPthY9L/hh1tXDXAJPLRti4En1WgS4TA+k6QNeio2EVTgpUhPrAl7EJ2uA443zrhNtHkybw0VpJd48cQN2HESNryghn3r/qzRP6gBetU+pOVwncCxJxFAA/OM12g+TT20R0SaaC7x7doYvCvC3xDvoePf6waoNDSGVPpUGngw3mAf5IoThYp4xHlH/8qd1MAyAObWMSj//Teh6vv+Yz3VVAKWsr+X7BOV9Kg18PA/2JjiS/6P+m6wb6QTBdZ/CvqwqmKYsOw+F0K2qV13GV9kcW5ap8smIkD5+vVGHpq3DsauEAJIRYxYhPav+llken6aJJMYBF9Mf5YELAejvD2r7xIt/m3J4lT7NFLgsfHExEivRYbhFgfeGHXmOOxc80JUN8dkCvCqfMoGL0x3kdwSOP5wnhORdhF4+6tboyuv1rZ2v+8eGAODPZH4qAly844bfhhdCDBngWDD9jNeyDXjPp6MqfEoF3husKyS8ztXk5LdOQ6XGoOmB4SoIOtenrcNHhZVoogzVsZX3rHW9Yev5dCrx6bSoTxNDugmmspd+0Wxip80Bd8Ad8ApM19kyB9wEf3LMADjgcwI8dQZAQZ/AAZ+xFZkBUAkc1qINs4EH33x3eeH2x3kUbWkzAA44gX/XoujWPMHOmgFQ9XDRy+Rv44GrOnkyS5s0A6Bk49hy8gQtOU9ttXDLMQOgSjBacbYMbR5Pj2bNACi5Hj89OtoeN7qc0ZXrdJvolVc3qJEeJcdP4BqtZnke13zCU8tOl8wA6MjfRgNHy/oakU3KPM8MQOXA8Rqy0SvTxU5/aNBKsVZgBqDqiiDt+zjGLxrf5Zbm8qEZgNNJMwCVC96Uxo4lIgf2dfWebTfe2MFvrqakC2t2Sv9Dc+7T2dmwJ82vWxUecafjR+4c9LQmS/rOtg74IKe776XL1yTnESS3YBfM3CI44M7m2f4HFZq2zsbi7V8AAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ 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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
…(2)
Thus, from (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 19.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 6x + 7 = ![](data:image/png;base64,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)
⇒ 6x + 7 = A(2x - 9) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 6
⇒ A = 3
-9A + B = 7
⇒ B = 34
⇒ 6x + 7 = 3 (2x - 9) + 34
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
Let x2 – 9x + 20 = t
⇒ (2x - 9)dx = dt
----------(1)
And![](data:image/png;base64,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)
x2 – 9x + 20 = ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
…(2)
Thus, from (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 20.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFAAAAA4CAYAAABqtn+aAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAQVSURBVHja7ZrLTttAFIZPmi202wKZ7LonnmTZHXKHctm5kFjeNMhCERqp0MoLBA67qBceoBugm1Y8QctlX/EM9AFoeYSkridOiEni2E5mUpIM0i8Fy2TClzkXn/nh4OAApPqXhCABSoAS4IP5ZwASrpItnT6SAGPA28rjAgK4dV87AOgWKeuHmmk9nmiA7k+kXWTn8Yp7b81VtaFaHWRKvTQta3oiAdq2MaOAcm7Y9kyv+yoVc2oRoW85na41r73RyaK7G38ziFgvL48kwEZOeuTPRc5dngrPT1EBlnfIPDHKzzuu63jZXc7BRnlp5AAyeKWShjFC30EpfGG/M3iU5IppgBtAL87MSmWKB8AgbanoLQC+7vfv/yvAsoGXWrkI3S6UdrGO8X6e2s94h3DQF1jAcIII3R7pIkL13Jqbi/4AUq4ItTO97j2th3urDaFUS7kALzRKU3Hbk93SgoIA/xS5+4YCkCV4guAcUuQiLGTdHXPkq6JN/e24hgtHvd7HssxpVlTITnl+LPpANxftACi/DMuaFVGF/arnWRVviCwcQwVoWcYsyWbfszDGeXtFJEAGj31ZiJS221PDSAH0WpVTls8SOiGvaZk+JSm4cEPvxGttnARvgGzNTRWbWN00/fnSNLUnahp/FpULxYWs27pQnbxs5iEdwzF7KnBbGwVjfZ8nQA8eeuc9wnUR1o9HageWCNoGSN/4nwxYW8P6P4QLH8KKiR8gBvwjDKC3XkfxudNINtJynCUlAUqAEqAEKCUBDhHg/YmHVJB6AaxKhYtrCE/qzuMJ0JkUiQY4UaHLG2BVVuEBAI4TkNa5jJYUDrCRXMcGoHeWAmcsohKgXGuWNScaoDNOALdIrnh/ABx+ECbzX4BsSjIIlKuwYa7Mf0EAvWn4mTCAUfKfz6+XGDWA7GA+R2hRWA6Mkv/cD4GZX0+kO0qEHO80sRjl7EZY/mMVjaTgUrS9TAQ8dqrYPIgKix5h+Y8ZHofhz+PdA7LjUaRusiPSpGVpc6pKXw0dIHMjZFH2q2HgjSCAg3oH+/i8oet1enPSN2H+Gu4FxLOVoU8sBDyDYydAHt7BuPBErRcKKm7+q4cu1j+y10EAeXgH40jkemHzPSdO+N6FbqN3CgLYVFTvYLtvMFi9PTdxvIqDAPSPppxuu7AbQGirXlEARvUOBvgGO9Tuyup3vUEBVv2v22EF7cy6I1RZP/TviL18ZpXdm8nvrQY11P16B/t+3uW8XtR+LxnWQAcYfGqN+2vdKtog3sH+pi3814sC8N4ujDNA6BbCvLyDcRpjketFbQOqzV0YZ4DQDSAv72CskBW4XtxHt1gD1Gb74C8svLyDUSV6vTgAq+M2QB1KDowzQJAAI+xCCY3TMEFKApQAH4L+ATX9SLwgFVRqAAAAAElFTkSuQmCC)
Answer:Let x + 2 = ![](data:image/png;base64,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)
⇒ x + 2 = A(4 -2x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
-2A = 1
⇒ A = ![](data:image/png;base64,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)
4A + B = 2
⇒ B = 4
⇒ x + 2 = ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, let us consider, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAA7CAYAAABMvWXaAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAa9SURBVHja7ZvPb9RGFMdnkyuEMyGzXEDiSHY2t/YWORMRInGwwq7lC0GjKFpZTRZkIRo5uYVS1HPpoYRDW6V/AflxD/ReqYL8ART+A5Ju5/nH4t211z9n7XWM9ASsVp61P573vu+9eWhnZweVNt5WPoQSYmmFhsj/VAr3sHJ6T0Iuypg8RanygO3uXioKwN1ddkmh9IHM2FThIeoAkNDviwTQMcNQr9br9AeZ6bkCmerFOtzdNAl+Qdvbt4saf7bb9PZ10niBUCc3rjXVi201ZpcxUX4MG1+4TYp8GJ3uGo7tT6RxXYWgV7ONreXCQdR1dpnOoCOibC+F+f7T9XmCEfoc9vtxAK41SBPW4AD5f/FnXFv5KQ1XuK2QJTRDj5iuXy4URA6lhhH+h2rGbEjgx/BwRUE0GuQu53jO1ziz7dyEOSMdJ334hkZn4V7n15/WCgWxJeFHCJFT1TCuhnnAfIf8KwoivCSLGP8xp7RWnM82FLqY1pogcAhCp1hqPSoMRJDf4EpNFxOgSg1dvlbH9d9VlTwUBRHEB1W3v/XZnR2ibt9BA/FShr8rcs9n3vE6yv2ODUTnzUSkuRdGvRLVuGPGFYHudIi3+ADeAkBXEfrISf5nulm8eNA21Bv8Pt5bMRSdw+/0u1aToL2wnmc8IJoxgguIAIimGyXN511xMEKIsMuatYnXmK5vunfUAkYHHGQH1CZ8x9qt1Y9U2VgMUqgglsJogDGDqLzydXG6Om26UfvNDYK4j9BEr7vzs3Bpg6WGyUn/zrG9yHsAIinKff4bfwuzu/iubhcSol+ghze8JV1vu91TEETurn51KUtfw7S1ERizbaHjV4QA18p//yeAElZxWhBHGw4iQfwa4K1gn9SdmukHz9HcO+hJYxbcF3djT5btz4Qk/bCjNYk8HBbfkB2ruVs9x9La4zAFCCu+5ngnguvhVP6CwN3QjJtJIbYo3ujfQRUnbzNzOR6DBJTqOqYHwO3+3QpgB1wtj9UKxVsgdJz4OOzalrDJMcQmmdizHna4hxtWnQ5UPQS6IwC1JhFGpDXm9gCMyVekKnnpxD3dSnnMOAhChyeTB7ZbJcNA5lqdmkCqCy+j5D9m3oTRYZS8SSRECyB+bKcKg2YLMOi4LGC8P8/0up03VnQ2X7dKdbXTe6x9y8u1dvNETA9zmSfaEH+J+uM0ijejvJmGSiDhPhsWq2Lngx7u223Oml/Fk+VxnNzR67seZcMjTLXNNFIfOWFx3ie+1d5FdROWwstPPVGkObXTpHEcPMb6irQE+oMr+3bKEMMVsvtdDMSTvNQThUKEggBePEjqSl0eo5MLiI6LrOCFw7y0aERVfhpc+KUVBlw5dj4gWnEGPycN425RIZo5r106zDnE+M1a063W689UXZ8uGkCzxQX3liCt6O2UyJNuiHE7K6lD7Erwgp52S3JPAKTN7t0iuPKW//sLwuRkZV1aciAOdlbooWY0bgZ1VoRALM3XFROMKp+cCpLRVm/wD07cwiZOZ6WEOMKdbB5J6ev0OEUPd0yM2lmJBDFca6g0twUJGL/Po3RWIqnTMK2h0nptoMzYp9z9IHY7K5XgzkrqKYZPQL+wO7ALEXJoLlj6iyF+EKN0VjxrpzWE36UMsXPRzLMmDXFuRjp2n321jnoCRNhtVv00amfFuwCO8FsBEC+kG+0vs5l91Nr91zJjVxhjU7Re/dnqmlTOUZ3+qelsOmpnpWcRSCohoV1w9dvSglgqVAfk3Gq3U4LpG02j31RR9e852vgOclC7s/IlSmelf7ufEkVhaU412TGihCiyntuTx2D0Ju2jEn4xYtzNXTrLDUSBVf+OX4wY28QdQo4pNuCsUO2DrBvXCg+xiHHN8VYKxLCMj/OLBlj4eBj3JMQ4QSxkPBxMycjBhYU4imlh0QbJ+hxtrRY2JgaJGtHTwqINDjoplK5m3TfNTNSMYlpYNEA4Xe4k3ll6k8xEjehpYdEA4XCyVe9Ek5omz1CqyUWE6BsPh00LJ5ngTfBbI605OLElZpZkJBC9Wi5B8TBoWjjpBG8cy2LNzCG63tqOH0jfXRhiWjjJBG/sKkwGa2YN0d1a8gTpBTHKtHCcCd6k08Vxp4bHFeKZ+9/9wLxETZxp4agTvGlMF8eZGh5LiD47c3KYqIkzLRxngjcNkTPqNfMCsWc3eomaONPCcSZ4U6jAjHzN3KQY7t0Ytl46zJ3GneBNYlmsmTeIXZGTFGLcCd5EADNYM5fJ/rDTXp5q0GdaOO4EbxLLYs28QjwrYif/Qggbv/SjtDGvnZZWQiwtgv0P51pbhAlKUUoAAAAASUVORK5CYII=)
Let 4x – x2 = t
⇒ (4 -2x) dx= dt
…(1)
And, Now let us consider, ![](data:image/png;base64,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)
Then, 4x – x2 = -(-4x + x2)
= (-4x + x2 + 4 – 4)
= 4 – (x - 2)2
= (2)2 – (x - 2)2
…(2)
using eq. (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
Question 21.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, Let us consider ![](data:image/png;base64,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)
Let x2 + 2x + 3 = t
⇒ (2x + 2)dx = dt
… (1)
And, now let us consider ![](data:image/png;base64,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)
⇒ x2 + 2x + 3 = x2 + 2x + 1 + 2 = (x +1)2 + (
2
⇒ ![](data:image/png;base64,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)
Using eq. (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 22.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x + 3 = ![](data:image/png;base64,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)
⇒ x + 3 = A(2x-2) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 1
⇒ A = ![](data:image/png;base64,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)
-2A + B = 3
⇒ B = 4
⇒ x + 3 = ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, Let us consider ![](data:image/png;base64,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)
Let x2 – 2x – 5 = t
⇒ (2x -2)dx = dt
![](data:image/png;base64,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)
And, now let us consider, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
…(2)
Using eq. (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 23.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let 5x + 3 = ![](data:image/png;base64,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)
⇒ 5x + 3 = A(2x + 4) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 5
⇒ A = ![](data:image/png;base64,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)
4A + B = 3
⇒ B = -7
⇒ 5x + 3 = ![](data:image/png;base64,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)
Now, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Now, let us consider, ![](data:image/png;base64,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)
Let x2 +4x + 10= t
⇒ (2x + 4) dx= dt
… (1)
And, Now let us consider, ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
…(2)
using eq. (1) and (2), we get,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 24.Choose the correct answer:
![](data:image/png;base64,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)
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH0AAAAdCAYAAACHdGN/AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAATtSURBVGje7Vo/b9tGFD+5a5y5cXTc3KwxT9qazZAuddKNSKgDJwccCOFQxwE4GDXlzSjcfIB2SOLRQ7YEbaxsHYJ8gbSw8wUcf4TE6b07UqYoijzZFKXWHB4MU9K9d+/3/v2ehHZ2dlAlV0sqJ1SgV1KBPguDEKoJWYC/FUBXBHRO8WMB+Bfc6m5WAF2h8t5j5F4FegV6ViuYuzYw762pdIUHql8n5GBhUtBd17rOCN4jTm9txrPHsO2b9DYhLLBc9/qs7EnalQzCUiN1d9e91sboDfTsIcHtN+7u7jVd0H3PutXA+HWT8QezArxrt9baxPgdIfLRCYIb8dc9MZdg3Hhtef6tMmyBBOjaTRtj/Jf4/7PyKXkH+re8VUJa/FEu6B3T7CUvMi/l3fedJYJqx9PK8GTmjhs2DQN9EKl1lga6vIND1mqIHDu+v1Sk7tHgIx2M0CcA2eZ8JXot4PYyQehIvOcrYb17maCLyDAxMt/PCnS4yM/2yo8C9CfJsq8CEu0jwp5PQ3cQODdMZB7q3r1D0ItxoIMwgp4js7OvUzkn1Q1nei0sfFQ7w8Tei1fKeOAhCLzEmSN9slVHb+Eilu/fTPaFRM+opfWUrH43CWWTQjrPRgMS/0N5sJKVLfFgObflYKFs0ANOV8DeVW/LLFp3YJP7kMVZCQBnEqP9WzIgRvqtKlniMOl4fAIO9n13sWPip7E+fIbNzlPX9xdVyXUXbUoeQ4WwtrzvYMBSfcV8r3NhXZFOrtN+WlTLyPcsQjD+A7IresZpc12Uv5Pk3FAG6OBTWkd9EbwvigRdgonQR4HPp6wEkO8jbDt3ek+7SPTM5sFyLBu/Rn1XvP5MBQs+bVL2EzhXRTk61bmw7hCY5UBVyqKgxKcQbIyQ7cjmWZT3QYkfE6gXBl0jyyeibMmLDCbuMFMge2AiTAKa9jkJksaFdQGB6M6jcpw1H0jbRJXJyoI0+uj71k3h+H7U2sZRyklA77bwJgRh0pYc3d9k6VZ6Rwe0wkBPUgNGmxuyXMpIKxH0sHLkgS71YnSooxcq1Ah9VO1t+FlitigC9FD350l1D/yacmahoAPYHYJ/hR4P5Zvz1TulZ7om6OeOzgajrPI+DvSL6i4F9IESTA8j8NL6dVnlPW9GAB5PG41fwD5iB/f/b6AP5gQo7zn3G0cVMy8CH4pl2JNh6qRAjw6eNuiDsp0CuqJlB5JGMkrXeY9/Gx/6dDeM0wA9fM9x3pmT6A6H1jNUb71NW/dGuFGnd0cLdBVF4fQLDuT0e7nxqbf7oADoGVAyOa0LasQZ/cHyPFPxe/k5AkphMFG0QnH+IiZ4yRpSgkhmU2hLlFFqam73BY0z02jLZRwfzTeUoJdwP3Xn0YHrnHHkT9mTBpwX7TPEwArr1mj48113CVhLk/J17fIeZvYJrPUiBw64LnzPTdgeD+xltUMXPd5x1of36YLbb7C74QowfEaOitjwgW0GMv5Ocn9FIYUtsV08ZAPYDPbqVhrVQsifebYO08Pxwx5URLBXp/fq6o7LBqN3G4bxKj4QGkbjVR5Nnclu/TKiVpsP9+f+68toTTqllfGlbPuvgR4OdEdNu2vPK/Cyp8oFSjEV7sqDHgEPZQ1TFkSr4HkSzpoPdcpsBfoFpvlZ/ohibL9XP6LYLoKxVKBXUoFeSQV6JRXolWTJv27jWBWS2dcmAAAAAElFTkSuQmCC)
C. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAAdCAYAAAB4+oTYAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWTSURBVHja7ZrPT9tmGMdfw46lva40r3dhU4/Eb3LsLfNMoZU4WNSxfBmThaLIGzOTVSHmcMvUqbtvB1qOHHYaVSvgtEMn/oBpY/AHtPAfwMjex2/exDF2HCCJw/oeHgmc2Hnf7/t5n1+v0fr6OhImrFcTIggTwAgTwNw420JoDCE0jtDWmABGWKpVNbwsIXSG1aorgBHWk9VMMvdBAcPcakMaqQEjJN0UN//BAAOLYtv6bZPgH4nlz2YFBgNWH+9YBFebJsT0ddu+Dd/JUjw9yFGi1h7vTQGmEWzCzjmwjQnW6TBiH+Da8/cLGL8qmtWFrBLGyoI69zmRf0GIHFm+fzeaH2BceDVvu/fTnjOoMdbr9i0NozdU1FNqZy3D2hu7Xr91E4BpMMdwZ8kgZYzx7625YPIHaOvZpQJRna+6AuN7+j0FSYeD8ix6xGMkJYyyjP6keJ/HAROM0yKzElIOdc+/l+ShyopSi7v3/xiSetE1upkCUJB0TAF5a7judEtb15oiCP1DJWwQqzabCAwTGW0iYm4MYlK+b91VkLLT6yKWCXqZBAyYSdAGUsqbcaFptVIiGCn7WQEDC/LUyD/G6tJ3g865LqsreJYlFdNxSeeYlJ9xj9gBO92QVPvD6DNjRMZ/a25tOmnX6pHeQjv+pRPeb2Agn4HxliqrJHzdo/mXmkN7CClHuuPkmrFZutgj4da5oDx3audR7bh+mbK65eJJeSMtXxumrmsUZPrsBnUML7o9k8hf/ByF6eIC5bTdOOJYvJsvKBi/5rsaxHS04qKM0Ltw7B4WMEEekUO7dEFeRnMLFs6kBsst5Hd8EwBMTxT8nOcc9Hv/YmXhJ9urT/DPF1TignfSVyuflQl+xuJ6fj8KZv/yiOHp6nnWpILQEUL4OMkxtIAh5lpildQWP546P3BRTGD6YycgnknI95brT2UVkpph6QWFfM/2vIle7uXXDcf/FP53NPwt7Daaa6w0P99gsOGTomZ+A4vFPBk6DoPZt3DCdD2N6srH129dfYM8SvMuPZXVAVGUvLQkzTGLC4F4WNnvRmic63ccPZdH+d1QmBjv1j7vBZiqil0QWnP8fNq9rcqmuWthfFAJ0PmchGGI3tvaTAnetx/WoWtkLv3Ulc0NNYhZm7seMI6WB+HSgGmKvtOLeLBbO0rOwENJ59FrSTG+38CEBYdy0tSKy3TO79mOyxaYK+h6elldW/OI0es6wKykJnTBIilHludNZlklXQUYlsN88hzymuJD82vHKT0YBQ8zDF37C0wzJKXFaUiaZgqFH8B9EsN/NALArPQKjOfZExpUT1jb4QvPN0rWwAxL1yDnox41b6w97la1JVWEF11iDDAsZm5B3JRMTfvSqTkf8+rkMmc7gwCm+Z3DpOQWrvPJx3nR1UpJ4cBwoYYFTBa6soYnTbBz6p5u23eiYMCYQBPNqj3oCkyrYgBRIhVH4CppyeeY2kOe6LLqRN2rVHQlrvy6zsR4y1ol6Fdw0SXbK8SJ1/QYu3GNxqCpx6sOuhihauc9F8u27eC8LKiKmvPTKxXCejj03uB3kQRJJStFWV+nryFoiLpGekRnEk2w4QiA/v0RJMmebU9ChVbUqoupIYk3wmQk/xXtN7AfoDE/dLYEpEKfIKlT2GVir9Mmxkv4tMQYdgKMN65aY3OBPobyNvx5lfc34F0VOnbXt6bYmRCdn2UtNs+Hzlr9m2VzhsJy0L6mHPSrezxsXcO2bGozRJZ/CyfPsky208r52Ax8THmyOWqvNcR5oQrkLyldVGH9tfgOH91RRaNqjOp7JwALa0CRgywPFwUwIWgKsryNNdOP5jOZD5jCUjWKhiwXti/TZRY2QGB4ZQDnKFm9QJVkzReo1gbZDxF2BWCECRPACBPACBPACBth+w+/W8zfkQ5jKwAAAABJRU5ErkJggg==)
D. ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 25.Choose the correct answer:
![](data:image/png;base64,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)
A. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKEAAAA4CAYAAACVOJg9AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAfFSURBVHja7Z27b9tGGMDPGbLksQVtEp+ADnl0tE5CpzYZDPkcOwU6CAlFGAXiQINgEI1jgINR096MIu6eZEmy1Fm6NWibZGvR2H9AWyDJ1M3Jv2C79x15Ek2T4kNHiUfd8C3Ug7y7H7/n8SPa2NhAWrSMUvQkaNEQatGiJwChCRA9Jg3hyBbLMukNSq1me3PzdFnGdc+ks9S0bqgC4tgCaNvtM7RWeVg3rVtlHJ9j0SmMZ7fbtn1GQ1hQAGcx3qaWM1XmcQKINVz7acG2LygJofArmJwomwluEbxFFtbnEnz3hE8KYdoC13QiCYgY0+dF1oiRC7VkNOZmSOUxQuT9guOcLwuESw18H1NrOVZbdppXCEY7bC72QSpk5tGoFzJ4TQiTnenOKon7nUXxMm4s3VcKQrjoSgX9wwZ6UCYIbXvhAjNP23HjWe1MVzFCH4S/6FjGJYrRSzRJX40KRK7REPqIqbkmgijLrN9CCH9kIFb7/XZzs30a3I+47xXSJ2wR9LRMECbRgrBgdBK9QqT19AgEzsJ5gtB7plFWRnXt/CbwRfHiWpNouXWTzAfHpCEcsvAFw/h5XDDS1TghCxs1H8G8nPClZfqRYJ08rUfE//IIn0GYxL+Fm6iKqi+LuJZjAyE3seCgx+QDfRCuhGojBoIAGWDodJqEYPwrqraeiWNWg9xl/7GHMH0pK//oXdcenL9hLM0B5FyzE/NB0v8wCXpCDOemhnCUpjiB2RJml5m+10H/z52PHoTrC2TOCxIOhG9mErJmWM6lHP3CD+x8h5OTk38CjGl+X1STXBoI40pVMBZirs8n1RgAFq62fmy222dB61iWMcWild2w+YAAAbQnwtXdOHPvM9VxMhH2W3au213w2Y0C15cK4gTWQEOYEcBWFT2L0nTgD85UyKM047BofdE1fzwV8oaadJFryBAT6/qbXvQcs8Ae4PtxEgygeNqsgVfA/ML5TIIfcBAZ+EmT0UX1C0sBoeu0M80VAaGMyQcA4BxR2tT1F/ObK8cgN/2ugH/cSU1s0uBMQ5iDz8f9vMrMo6xmCPKLUVpQfE5rtR/AJOfl+EetBT+eQAP3vo+3xhbCvEuAfSHM6AvBNUOVgvuCmOz458FX1pwwKV201q1P/flF2WU+14yztfCZXmGi00ThykAIg2u3m2cpQT/DwP25qex3Mt6C/8oSOfZx5ifygJDD125fMChZ5tFoyCJz81ttPeNbwbxF5aAwrdTpNKuEmGs5RMZ78P8iWILSKhxLkifMEqDJUDphde4gS+GhfC/10BNiPhnsTgZHmrxNC2HX6Q9z4H3XJAtC//kwrr2g5r3ZaD8U7/m3gsG8ARQQPOQRgcI4CEZvfLXjN2m1Wt4QCgW2ZNQNjPEf/jp3s2NfWe1ME9Kw7iY2x2XJAzrfXv3m5MnP3zFz+klZxptVrp9Df527vr6cFKi0AHL4uPUgO4ZlTfVuIOMSM6fvIMcZvAlKMbHd9EVjaSVs4jSE6SFMm1Ho+qeQpYiwBDxZjsi7Y2VPyTAc8dXC6qlRwYrfh8iYognNr2kIhwOhm0JCh/3ctqgshbTB8TSGt9etUqMPPefcgc9WO83LsDcRo+quGBQU313Hv7rbXO1c9pKv+5B8lb3lqKiVglFIUp8wDYTdUifCH/r5qPx7IQGb3MF5Dqeb0WeRImk99S7wbXBvoiiNQQK2Ts3vABCxeUB2fVNDmDOECbRg6hRN6kX27gRI1AoTHKQ+LOcYPNbdy5ci+aohlANhMKVi282LAGHTti/G1bTddTwecGSCMGFh/Zjf5ktrHFbIzGMIxYPfUQHCNOMvqmSFMKKmfXA8LWY8Obb2sGaBkuIgEO4nleMLzULwXg7rIOjbKQLhvuoybHMsHcJB0yQCRnieN+gDanNcXp/Q06KHWevmUgYG8DRI43v/JlA3J9TzEzSE5YXQq7BF7m8EBQVrQA3nq1whBJ+QJykZiG5ds26IxCSvQ0+i1+Ju4bVZ9/mI12JHsnusedEN9cl7cIg1hGpAeCRXy9wwEROAOO32edhtXqfWYu6akFLzjmVNf9n1C726Zu/ZCP+GTXPtaD0Y79F75qyXyvGOkbeytpBpCLNBSBD5Lc0aQA+cWqXyy5G1xrUXcfsFxmLidcWkJ2lqx8MSDaGGsLgQFrEPi6oQps3laQg3itmHRVUIs/aPGWsIi9iHRVUIB+kfM7YQFrUPi6oQDto/Ji8I8byzWFgIs/RhUQJC64trp05e/XfYEA7aP2bcIYztw6IchAj/N+84n43AHA/UP0amgBYmp9Df+GvnTnEhTNGHRSXJ0oFBMoiZ+8dIvRZVOjCk7cOiisAjp6MIBgbtHyP9hlClF02aPiyqyCha5sroHyMVQtgBPeCju0ODMMQf7NuHRQ2/kGkB0toa+qIP2D9GrjUYzoPv0iGM68OinF84RA0kq39Mmf3BvhD268OiqngmeWi5Tln9Y8psikMhTNKHRVmT7G5P+n1Y2lBW/5hBhecmC9gSLhTCpH1YlNeGzDcc1qYMGf1jBpWk724pdGBSNoEotYgNxPMQt2H87HaRrdlYQuh/uUzZXjMbBJC/267o7Z7HEUIBImjEumndLuP7jrtv+VTAnx9bCIXwdwOX8n3H6vjzYw+hFg2hFi0aQi2jl/8B56EILtExNNEAAAAASUVORK5CYII=)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Integrate the functions.
Answer:
Let x3 = t
⇒ 3x2 dx = dt
= tan-1t + C
= tan-1(x3) + C
Question 2.
Integrate the functions.
Answer:
Let 2x= t
⇒ 2dx = dt
⇒
⇒
Question 3.
Integrate the functions.
Answer:
Let 2 – x = t
⇒ -dx = dt
⇒
⇒
⇒
Question 4.
Integrate the functions.
Answer:
Let 5x = t
⇒ 5dx = dt
⇒
⇒
⇒
Question 5.
Integrate the functions.
Answer:
Let = t
⇒ 2dx = dt
⇒
⇒
⇒
Question 6.
Integrate the functions.
Answer:
Let x3 = t
⇒ 3x2 dx = dt
⇒
⇒
⇒
Question 7.
Integrate the functions.
Answer:
For ,
Let x2 -1 = t
⇒ 2x dx = dt
⇒
⇒
⇒
⇒
⇒
Question 8.
Integrate the functions.
Answer:
Let x3 = t
⇒ 3x2 dx = dt
⇒
⇒
⇒
Question 9.
Integrate the functions.
Answer:
Let tanx = t
⇒ sec2xdx = dt
⇒
⇒
⇒
Question 10.
Integrate the functions.
Answer:
Let x+1 = t
⇒ dx = dt
⇒
⇒
⇒
⇒
Question 11.
Integrate the functions.
Answer:
⇒
Let 3x+1= t
⇒ 3dx = dt
⇒
⇒
⇒
Question 12.
Integrate the functions.
Answer:
Let x+3= t
⇒ dx = dt
⇒
⇒
⇒
Question 13.
Integrate the functions.
Answer:
Let
⇒ dx = dt
⇒
⇒
⇒
Question 14.
Integrate the functions.
Answer:
Let
⇒ dx = dt
⇒
⇒
⇒
Question 15.
Integrate the functions.
Answer:
(x - 1)(x - b) can be written as x2 – (a+b)x + ab.
Then, x2 – (a+b)x + ab = x2 – (a+b)x +
⇒
⇒
Let x =
⇒ dx = dt
⇒
⇒
⇒
Question 16.
Integrate the functions.
Answer:
Let 4x + 1 =
⇒ 4x + 1 = A(4x + 1) + B
⇒ 4x + 1 = 4Ax+ A+ B
Now, equating the coefficients of x and constant term on both sides, we get,
4A = 4
⇒ A = 1
A + B = 1
⇒ B = 0
Let 2x2 + x – 3 =t
⇒ (4x + 1) dx = dt
⇒
⇒
2
Question 17.
Integrate the functions.
Answer:
Let x + 2 =
⇒ x + 2 = A(2x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 1
⇒ A =
B = 2
⇒ x + 2 = (2x) + 2
⇒
⇒
Now,
Let x2 - 1 = t
⇒ (2x)dx = dt
⇒
⇒
And
⇒
Question 18.
Integrate the functions.
Answer:
Let 5x - 2 =
⇒ 5x - 2 = A(2 + 6x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
6A = 5
⇒ A =
2A + B = -2
⇒ B =
⇒ 5x - 2 = (2 + 6x) +
⇒
⇒
Now,
Let 1+2x+3x2 = t
⇒ (2 + 6x)dx = dt
⇒
= log|1+2x+3x2| …(1)
And
1+2x+3x2 =
⇒
⇒
⇒
⇒
…(2)
Thus, from (1) and (2), we get,
⇒
⇒
Question 19.
Integrate the functions.
Answer:
Let 6x + 7 =
⇒ 6x + 7 = A(2x - 9) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 6
⇒ A = 3
-9A + B = 7
⇒ B = 34
⇒ 6x + 7 = 3 (2x - 9) + 34
⇒
⇒
Now,
Let x2 – 9x + 20 = t
⇒ (2x - 9)dx = dt
----------(1)
And
x2 – 9x + 20 =
⇒
⇒
…(2)
Thus, from (1) and (2), we get,
⇒
⇒
Question 20.
Integrate the functions.
Answer:
Let x + 2 =
⇒ x + 2 = A(4 -2x) + B
Now, equating the coefficients of x and constant term on both sides, we get,
-2A = 1
⇒ A =
4A + B = 2
⇒ B = 4
⇒ x + 2 =
Now,
⇒
Now, let us consider,
Let 4x – x2 = t
⇒ (4 -2x) dx= dt
…(1)
And, Now let us consider,
Then, 4x – x2 = -(-4x + x2)
= (-4x + x2 + 4 – 4)
= 4 – (x - 2)2
= (2)2 – (x - 2)2
…(2)
using eq. (1) and (2), we get,
⇒
Question 21.
Integrate the functions.
Answer:
⇒
⇒
⇒
Now, Let us consider
Let x2 + 2x + 3 = t
⇒ (2x + 2)dx = dt
… (1)
And, now let us consider
⇒ x2 + 2x + 3 = x2 + 2x + 1 + 2 = (x +1)2 + (2
⇒
Using eq. (1) and (2), we get,
⇒
⇒
Question 22.
Integrate the functions.
Answer:
Let x + 3 =
⇒ x + 3 = A(2x-2) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 1
⇒ A =
-2A + B = 3
⇒ B = 4
⇒ x + 3 =
Now,
⇒
Now, Let us consider
Let x2 – 2x – 5 = t
⇒ (2x -2)dx = dt
And, now let us consider,
⇒
⇒
…(2)
Using eq. (1) and (2), we get,
⇒
⇒
Question 23.
Integrate the functions.
Answer:
Let 5x + 3 =
⇒ 5x + 3 = A(2x + 4) + B
Now, equating the coefficients of x and constant term on both sides, we get,
2A = 5
⇒ A =
4A + B = 3
⇒ B = -7
⇒ 5x + 3 =
Now,
⇒
Now, let us consider,
Let x2 +4x + 10= t
⇒ (2x + 4) dx= dt
… (1)
And, Now let us consider,
⇒
⇒
…(2)
using eq. (1) and (2), we get,
⇒
⇒
Question 24.
Choose the correct answer:
A.
B.
C.
D.
Answer:
⇒
⇒
Question 25.
Choose the correct answer:
A.
B.
C.
D.
Answer:
⇒
⇒
⇒
⇒
Exercise 7.5
Question 1.Integrate the rational functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGwAAAA1CAYAAACk5w7yAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMdSURBVHja7Vo7UiMxFHwH4ADrKkTGAbBMuqFRbXEA7ClHSxFRSjiA7MxVFBcgI9xgY4LlBNyAgBv4DrsrjQeGQaORxpItoINO+Ex1q6Wnz2taLBYEfBxgEGAYAMMAGAbDABgGwDAYBsCw3pBycjRi7J749O7lZ2N+zohWtC8eLpbLPRiWCeYFPyWivyXYSkh1VHCuJlIdYoXlvMqK4zOzotjwUZuGkpg5lsuLPbFPD5+lBH6JQ8flmF0R8eeZUgMYljmUmg0E59e6LPJifgrDMkchxE85l99MWaydFmFYbiXwvzmyED+qg8aU053ex/RRn/NCwbDs9iy2Oi7kWf2Yr8si49Obz3T4wOsBDANgGADDYBgAwwAYBsOAHRr22k8CcgJWGEoiAMMAGAbDgPwM0xmJKWc3OXVvlRSmx+XTNsmR/yaaOj4yOdQ5v3qfadvQTckTfnDbzGjoHhhjo3tXjC0H/q861mmudQzP1qfz0dRulpoNONHzLmdmKYCeSpHvQzVlFtEetsmB/1ueljuWJdnl0uQ0zLTYE2Qi9EAOafgnJNFkuLSIaOOZin+oBhO7Y+xXfZXrqlGtNtuEcnFvraeM2FOKIGZsw2xcU/IP1aC5iIn63rbqbIa5+LcPkCOIuUmGPbZhL8HRGpeU/PtqsJX7EE2thrn++H09Ds+wxzasaVBq/rEM05zZ+PLKqdkyeVoPG66PvTn1BGbYUxhWpaY0j9T8YxhWlrzho+v/65rchpmP0apLsG+GvRxsj1dpxwEhyLDI/GNpaB5CuiZJdMO66vDOVlhi/puuML1X+lw1/A1bl5Su2dI3w76tkpiK/yaGmXulx0QKMqxr067QN8Oe7NCx/n1q/n01mJU1lufNsT454Let90uL5nZ3LbU9RoY9VKwxYES/NXlb3bcZlJJ/Hw3lavHf94KO9a6LW4wMe4hY65NOQ0TIxTlWBj9Eg9OsWBfn1E87sd8bt/00tStNXo+/Obx0u1eg+/E3Z/6hmpyGVaL1Ew4Tfr2nbcJcfLvaKxnz76vJa9NHAzMfTR+uvn91YBBgGJAS/wAiAw0IujQWWAAAAABJRU5ErkJggg==)
Answer:Let ![](data:image/png;base64,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)
⇒ x = A(x + 2) + B(x +1)
On comparing the coefficients of x and constant term, we get,
A + B = 1
2A + B = 0
On solving above two equations, we get,
A = -1 and B = 2
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= -log|X + 1| + 2log|x + 2| + C
= log (x+2)2 – log |x + 1| + C
![](data:image/png;base64,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)
Question 2.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOQAAAA4CAYAAADtq1TZAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAXvSURBVHja7V07btwwEOUBcgAHWKaKD+CVXaZVBCO1EVvYykEKIyAQ5ACyOwOBL5AuB0idImnT+AYucoPcwdmRlrtcLiVREkWJ0iseYOxHqxnyzTwORzS7u7tjAACMA3ACAICQAACAkAAAQgIAAEK2hEiT87fRq2+MRX9XWfYSPsF4gJAD4VPMv3DOnhhjzyAkxgOEHAmuIvYdhMR4gJCYAAAIiQEHITEeICQmAIDxACExATAeICQmAIDxACExATAeICQmAIDxACExATAeIOQEcX//8UVyyn7QBEhEdgKfYDxAyIFwm0bvijYtBdHVd/gG4zEoIamHcOcE/k+PTIeOOvwMAACOM6QkJo8/fdHfy7LVy4ixv6b3AABwTMhcu0fR1yVnj2yR/P54f//iMEui8AEAXgiZieQkitKsyJKHkjSvfGF9BQB+CEkZMEpv30lpqpIvz54L9pveP/ieEEdXEX/Yri/58vFSZMfye2ly9nmxWPzRCS7i6IN8jYIBZ+wf5DAAQm6QRlEm5ai+D1QQZvmoy1UicU6k6OqBJK4kLklecSuO8r83RFXJVlyPP6kkzUk9wwxc+FqrLBqAYDUjQuZZcS1X99eL7FlmxFzGamSRWU1/vfjuTvKasp9Iz97Ta2rGzSWzIQMDwOwIKeXqHkE3stUkV7eZ0FDk0deg289uiEsSV2SXx3R99ZppklzrhSQAmCUhSa4aizhrwqUiOdflatWaT5e7qowlwt3c3LzWt1DoenX7mjaybszoZTAD98kcUUvIQq4mX83bHOyZCjI68XRJWydjc5KuCUlkVNeadF36e7USb+YaIbGGRIZkOomiWHwwEpVka2nnzv7rOxlbsmWiVV+ljBWr1Zs+pOrufnCiHBAIIau2M7brQUOTgLrGlBmviPTmljrTdXSSmohtChS2ULdVZIbGGhUYLSF1qWRslyMJWiKV6L28q2fT20pbH0LcHtWRQ/19UyDoI7OVbdtMFSKOL/RAN0aUqbPQbWtiV1ATS90b7eSgdUZfsuWvORDSVKAbM/K97HUwn5pttnYFM7HaRE8f1xoz8pO/Ayz+2Nx3iLbZ3PPojSja7ZLrJBXnzrKGhz3OTFwe7yQ8e34Vvf3mc806NlmuL2mqAmKhYPhjWfYbk20u7QpOsrqKUn13AMntnrNUvJfkVPdefdg5puZ/8sdZkn6WBb804Zlpm8z2/sdim2u7ZkdIVTJQtIpjcdFHRlc7kdTo6Ov5URkQ+gw8tuvwfF85Xl3Y+Ehfc5mKeD5ssx1nl3bNjpCHG+79nHLQpGupz8DT9ykOXQpjaiNI06Diw7auwbiNXZMjpBCXJ6ec/1SjE22v5J1CHqViFSF9TSYb4nf1VxdC5j6qqTiaHvvzZVunsW9p16QIuX/GTzHhqSQ+xP7U1uGGga9qlnAumSsmngt/tSEk3VvxZA9/qivSmezwZVsbn3exa7KSVT7GRR0/Q0oaKY/lc6EyahfVuH4la1VAcOmvpoTctV7a9eOaniDyZVsrf3ewa7KEtImg7deczZq8txJpc2pCkibXtpPJhWS2qUI28ZetP+p+d/9EifLgZOqFHtq2KqJ1sWvSRZ1inTa+5nF5gp+vLRfbbYG2/ura7VQn37sScqi50MauyRKSJgmdlDeGsnhbGemMkJaFmbb+6kpI0xNC1oTs2bbu9QwQMgd14GzP7hnNpvimY4f76SxpQv4u/nJCyIp77LqGHGoutLFrUoSU5/uINDnXH6+iQop6NpBP0JqCTtjzve1St3Zy5S9bQsqsRq2DstJJv206ebDODl+2NVEiLuyaHiHX6V+2qckopZ5+N0hhiYoA/PSnyx7cZusYcwR25a8mnTrqaYN1j+YdZPoG+5A+54JruyZb1AHq1zFB1ANKOlpCt202nTrAYRQO+RjN0l7WwG1DL+tMEfq/egjhaY8+xgWTd6pZMuBjSkJ6HtKlXSDkxIETA8KzCxN38tKVP4S03pL/dW1qttnahUk7A+DUuXDswoQFgBEBTgAAEBIAABP+A4o4AXz4pmbeAAAAAElFTkSuQmCC)
Let ![](data:image/png;base64,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)
⇒ 1= A(x - 3) + B(x + 3)
On comparing the coefficients of x and constant term, we get,
A + B = 0
-3A + 3B = 1
On solving above two equations, we get,
A =
and B = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOQAAAAxCAYAAADKpAURAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAT4SURBVHja7Z0/TuNAFMbnABwApAxdDpAMabcMFqJe4VipQFRopBUHcOgirbgAHQfYmmJpt+EGFLkBd9jNs3fs8WQc2/H/+Cu+BjnO5H3ze/Pmjw17enpiEAR1QwgCBAFICIIAJAQBSAiCegmk9JyrS3H+wpjYLH3/DAZ1T/BoIEA+zPkj5+yTMfYXZndT8GiAJetCsFeY3W3BIwAJwSMACbMheAQgYTaABJAwG4JHABJmA0gIQELwCED23mzaf+u8oQ20Ma9HiBeABJAAEkBWpfX6/sS5YL/IbEf6k6zrfemO6RgXZ9OPJgBGByvmEeLVYyBXnrgOj2RpEovXVBj95ZlgbNPkMa62zfOlM5ly9hH+Zv4l5vKuyTYW9Wjo8VIJTHqzm9Fo9CeKGZ9+uNIfU/vMNmGBoSdAknkzx/txv16fkMmew31qj/BW113N+EOPF4HIGfsKAZQTvbJTg8lOewBkex2MRvkpm/7Oajt1qOV8+X2ndByxd3OEytPGvN/bVyC7EC86iE/35mLxTEnBXm3s9lsA2QMgU+dy2w7G5w+PALJb8YpK+6wp1/nliwnrUQJJJcEF5296zW4uQIRlzOxHUFJsrzkXu8HJ6mBSupPge7TAy7m4C+45ct6z7lcGDCrJKPseAkGbQJaNWZkStol4xWsb/GvfoldwnfD81EWdsGMbE3aLzAzTNSCDwG/NVe0kONXEXq/Xw5IiDBrBmfj9KR1DNy+5wBHexxPCp8l6nSOkWiTgjH86nrzqE5BVxOzQRZWm4pVndNwbs2MaIaN5ggGUglRdF2UxLWjqGnOSnZnxtYl7nq2aMmAkV5btCbIPJWuZmBWNb9PxUol9Xz9qBMi2RlgdyAg8IztFoGojogmuObLm7WBpSaBMjLKy60rK04Xgz7YtH1sbq/reqoDMG7Oq+lRT8TL72eBHyH3lgpm56FoCcObJG31VrOgIGX+2+MJS2ZEq/E1J8/uyqHNozMr3lfriVSmQbY1wuTLRf+UeIS2Z12YGZc34HTE8grNIByOzHCF+ZpW7dYARJqB6gSzjT1pbysSsjJqIV2dK1k7NIY2A2Eqk4IVNBZOLzTzPcW7lSp7a9rgaAdJIPn0YIcvErDSQNccrqtL2lOM0cDiu/+3ogLQBGK/kiY1avdNXVM3P7WhPIJV5wf22HYleiajuGSSG7WdpWd+2nF3GaDXy09aM+k303XQcyyyNugpkVTHLFdeW46WmP+qInD6XpVVl2xG+3gMZr5zultPJM4zbv/OLN3NpPdr7KlCWJ4A0Slw1J007mVHN3CTeMqDvkXJ1WmTe1jqQFcSsaKJuK16UABJ74Sn98OhK1kNFQNom3rQkn5bB8PRCf9vSlzYOEkbbXCIeed2x69pXyNDBACSArEGqfKKRMHmAwB07jneLDgYgAeS+GryGM47BaZFoy4Mm4PzzkG2PoXawPP4gXkcApL65mjYRh3nttbGIP4hXz4GMzx7GWxYwrzttLOoPgOwxkFUcOwKQ9bXxEH8AZI+BVBv6XXu8C4I/gwMyzr5i43jObdaLiSD4AyCbmDtqLwPSHxpGVoY/ALJJw1OeRdQXEfDaevgDIFs2nGR7bAqCPwCyiZLI8ihOGw+yQvBn0EDGmXbX2ODvDT4zB8EfAKlnYeMhYpRD8AdAtiRauaN/nlPk+TEI/gBICIIAJAQBSAiCGtM/kDPFTBxaTX8AAAAASUVORK5CYII=)
![](data:image/png;base64,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)
Question 3.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ 3x -1 = A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) …(1)
Substituting x = 1, 2 and 3 respectively in equation (1), we get,
A = 1, B = -5 and C = 4
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= log|x -1| -5log|x-2| + 4log|x-3| + C
Question 4.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ x = A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) …(1)
Substituting x = 1, 2 and 3 respectively in equation (1), we get,
A =
, B = -2 and C = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 5.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ 2x = A(x + 2)+ B(x + 1) …(1)
Substituting x = -1 and -2 respectively in equation (1), we get,
A = -2, B = 4
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 4log|x + 2| -2log|x + 1| + C
Question 6.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
On dividing 1 – x2 by x(1 - 2x), we get,
…(1)
Now, let ![](data:image/png;base64,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)
(2 – x) = A(1 – 2x) + Bx …(2)
Now, substituting x = 0 and
in equation (2), we get,
A = 2 and B = 3
Thus, ![](data:image/png;base64,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)
Now, putting this value in equation (2), we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 7.Integrate the rational functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAA1CAYAAAB2twSqAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOaSURBVHja7ZuxTiMxEIZ9PfQXhNNBnzi8wWlvhWhzIrFSgVJEyA3FFimcdJFOvMBVxwNcC9LBE/AEdxI8QfIM3MWbLKyS7Hp2Y2+8yxR/s8Ay489rj2c8ZDweE1S5hYOAEFEIEYUQUQgRIaIQIgohAhwj5NOmZ5ueI0QHNRi0my1K7wnr3kbPhMcuKSFTQv2H/mSyhxAd1oizs/nX9jrXP0LozBeywRmTHSGPcDktmQQ/OZ9/eTNCm08KJO6JJdRk0t/zD8kjOfQfq7Z8fqjo9Mqj14Swl56UNYRYQknZq/mMfVdLKuOjM4RYQnHfvxAj8TlcUmNRKkIsw/I5Bya4fxoFM11GbtW+KESnwRiXCLEUeyCdnnBxHj9yqPMhZd2bqgY4lQ5sPopwEBAiCiGiECIKISJElKMQo6Ipym3pIL6i3Fehy2na7EGVYE98q+eFs6f65aBKQlR3WlaT0FUvzlY6OpXCb1DSfMKvscwQZa/WJM0HhLgjiEHQ3+8yerNNdVx9icwTl9adiQVQ4f9kXPaDYN+2f6Ztz2K/FuJw0D5W9zfj9bk8UlV2m/uhKgJ/ZfUfqwGUqi9S2rpvD4bHNv2zYTvEfi1EtQQyQl62naHKkDzvgB5L1PvrdfJncc90fSAW91DXn5vyb9uxSbM9zX4QxDCi3PJuSjiTvKtrBSQIegeeJ77Z2kNDexOc3eSLCf9MKc12iK0p0ST9m3bpVtfrsDAsnmmgU+glXtMQV/2B+AfxsSiIOnuTX5pyrrPd62Aa4lviYWkv5NxaZD+HDuKq/VqIuj8ootfBNMQ4OMg1xqL7OXS26yZeYkCj9rL0qMpsr0M8z6r2zxBiEBxA86+6gVjehJsD4acQ/7L6mKf6kAXiu/3rdiSsv2Smc9Jkr8P6/hl9BSvPUr4eMETuX0D8y+IjZ+QnpPqQ9D93BvH9xeaT2zaW0zwQbfpoF+JyOdWF3zZ7HaxCXC6nkONFUf0cxiHqApt4FsZWr4O1wGb+844UR1Cbi+rnAAc2Cb+TTH3DPlBUr0NWiCr/6bfIL+Xkl8GwqZuYSf4V6SPU9lxHjLTDZVG9Doslnf2GQIwdBxIDoCyH/SL7OSC25z7su5aWMpGjdDntlsd+EMRlgPO8ywy/udnOnhMS4M77l2Q/CGLkaIvSO+pzWcarFeFhnbbukjItrvunsx8EMdpUXSiaZt5Xo6KqBo6r/kHtB0FEuS8cBISIckH/AUqLzonckhfNAAAAAElFTkSuQmCC)
Answer:Let ![](data:image/png;base64,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)
x = (Ax + B)(x -1) + C (x2 + 1)
⇒ x = Ax2 – Ax + Bx – B + Cx2 + C
Equating the coefficients of x2, x and constant term, we get,
A + C = 0
-A + B = 0
-B + c = 0
On solving these equation, we get,
A =
, B =
and C = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, let us consider,
,
Let (x2 + 1) = t
2xdx = dt
Thus,
![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
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Question 8.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ x = A(x - 1)(x + 2) + B(x + 2) + C( x – 1)2 …(1)
Substituting x = -1 in equation (1), we get,
B = ![](data:image/png;base64,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)
Equating the coefficients of x2 and constant term, we get,
A + C = 0
-2A + 2B + C = 0
A =
and c = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYcAAAA7CAYAAACQYUbEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAwmSURBVHja7V0/cxs3HoVTR1fbicEurmOCalNlqHWclPSZ2lETOyw0mp1zlBkWnjHpznNx0kfXOF1SpI3nYqe7ItYncGbkL2DxK9g6YnexWpILLLB/QIB8xWs0I2kBPODh9/ADfuTx48cEAAAAAPJAJwAAAAAQBwAAAADiAAAAAEAcgI0lKiFX8kCftNvP6AvwGgMEOI+j4e6QEjKbT54LQuiMdvd/HI3HO+ibZhGFwRd7rHNCCHtzMB5/hD5pu7937855fe4qrzFIgNOYhuzL+eR5v4QLcj14CYFocKEK6LedDnmdLFQQB0u8flfA6z9d4TUGCnAWT56MPrxF6S+7YXQ3v7sVuy0WTr9EPzWLfUZ+hjjY5/WDMLiV8Xo4+QriYLuxBb4ePFZ3MYmCm8Fw8plk1wVxgDhsIq/fQxws4/Bw0O1R+pyw/Z+zXWif3Y/VmgYvRk+efAji+oGjPj2eL2BnB5PJNfQHxGHjeO1I329Fpy/61nT2+eHDbsjYZBhNPgEp/VzAaP/oGH0BcdgkhIw847x2xcnYqs5PswNmhHZPg2hyE4T0MySnhL1C1ABx2EheO9TvWzUA/CAouE5expkusJG8HD9+kAdhhziA1xCHxpH6em+w8/Qw8uuz+ziEhjiA1xCH5kO3ycG1gLHvubWERcY/UV8+Z0CWGcTBe2EI6LfL5ww4c7DZyLSzwyC4F02jq7G1lMtaAjzYWfWPvsk/MzAej3b2OuwEESDEYQN4/UGe10Gn95ML/b8VO04uBPzylPD04glwPXgZRcObjIUTENXx8Ytv7RYAAt8o4oWpR37j4sAz+hCZtc7r9zJeu9D3WzII9Dx/G5GntvL7DZSFT3Ew7XbIXfB0RgZYg82h8JkSiG+bvH4n5TUuwQEAAACuAp0AAE1OKFgxGAeIAwAAefBsuC7pvsAh+frHgRH2Bw7VIQ4AAHEAIA4QB6BuuK0D9BXEAeIAcQC2CPxxL1UGkAAetoM4QBwgDgAANBCFjccHH8XiMF+UEImtfxwG4/HHGIeGxEHXcgD8wDptqW3oT0kUdqFzXwD8bI7TJuMgK/YFrPbtMmHfA5uDOou7QhzQnw3YSuBnZVzRGQddW0l1GW0L8cHW2EoIJ3HmgDOH7ZubOHPAmYMSce0GSl4kix0eEgMgDtsyNyEOEAcl+IuHyw/t4R0lAOLgwNwMdu+JuRlHsnxujsc7EAeIg/1JG5fg655i0roi3P07rtbv5lxh/eh+FbsjW5TAM8O52Wx5TNviEAXBwJd69NPj4FNdfmNHB1hFyNjE9TKf8au9bP8HnFXZmZs+C+qcz498K1s7PWC3+YvUhFxcgTiku0FMxhZCT4P02aJqbuv+bvluMKnQhTFuf27uBtE937ic57NLmwjdNhRVoDMWh02wAHgFOJPzBpfbXLUP2sDDw8ENRskrkeHUYXsnMu/YJWuPF37aY50TVS3xJNqkp7zojatjv41z0yKX/6M6B2nDDqvP6927vE5NcseDzmh3/8fBaPQPecRGX6n4vTEWgErdTYrC+NBmF2yQZHKQmSiiNImGn8QZKJLDxTgpwIHiMXzH1OmQ18kEkotDwgXyzNWCN17Mzdi+kPPSdG62zOVzXS7n+dzmnDP522mxpncrFwGv9/+UtUHwW/Z/vLAAymwAWfH5+c+/m//8O3Glvt+P7vhie5iGiTa/PU5FLKjDnexGyBve50VC4lLltqxWskIckglnJw26ip3h+ryU2Rfp3DyWzc046mDhpMkMJiWXuRAsLZIpl8/ENxaJSZsV20wO1XkbblH6Cxc38a0PwuDW/BvfcoGQfScX7zm/z2T/g7huAcSTYdi/rbIBhAWQ30mtXvai56qdlosZTUfD3SFfVLMwcb4Lk9o2Fm0QsdgXLVBFi25aqnVWttMtWmjauiilIw6ZqLVctjFeDDNLg8540flSO8M1e06ywBTZFzpzMxYV2vt9cPjwho2ooUgEku9cbZsoPVw21+rw2UQceBuC4eQzSTQhLTtaJnJEFTI5sUDOB0LHBqj7zTbaXCFMXH0vRnFfw9a4qcShSAh0FuLDw0G3R+nz/Pfzuyqxh0qDF0370lrikO4e2+zT5EA2/BdvH98BhgF9pJrQztpzikWszL5Q2VKqnW3b4iATAZloyPgs/i6/3xHv5jXudTSRjpvUqpb3X57fpW8ruWoB6EzmzAKosKOy0WaTdNok1KW/Cg9U7NLEYZPsO+v0gXnIS94UkTwZp0txyCwohagtCiGd8cnIPfU2D1t1xEHn2+taGgf9gzs6lp3z9pxiEatjz1UVFkMunxVxORGBhI8rNpRigU9ETfj/8e8znvJqwucmxIF/vyojqawtRGfn54MNUGfi2LA9TMShJEyUioPNxUNYA8Lq4n0QRcObXUpO8+O0ICQlC2yabTEjtHuqOxZVHxA0EgcLgrs8YXWjMmfmpWIRq+PR89/tkM7rNu3SjMtpdo/gcmL1LbZNJSYFfP5nEvl2T3UtqPyz41wcqj47ntqPf6nG5fIZk+LxqzRpXLQBskWoQshtw/Zo4iJesji00weVwlbRfr5DouxVEAb3loVACJbON5ns1Os+IGgmDnqbpSbw8PDzriz7zpSnmZ1hY16qxKHEvtARy7YzgzLLJ+Vyf9i/XxQdC6HT+R6dKENgqP3s+FDr//ID6jJBuhSHxeioUBx0J6eLNkBVC8CW7dGEOPA+UGWptG2D6InXYmRjIg46ArgWW8mCOIzHo50kAYH+3R8e3V5eAJy353R2qBXfUGrj/SVNLq+c/ZiIQyI6at+/DVuJC52Oe2AkDiYWgIkN0ERxGm1xMFxYbNkedauE6WSprMMGuVzceBg878el3WkmDhr9y8ci6PX+bcMac0kcsp315W7xYiUd2IynmZ1hzZ6rYV/o2r62LiSmXC60jjJx0DxUTvlsbKlVFQdZ6nB9cTDc5enuVJuoIaAvDmYT2bLtURAmhs/0FJ7+WtauddggiRUyuBGfNdBV8dJZ1AR5+W3ZaBpdlR3Irk8c7IjtNIquhow+zZ6yzv1PY56Knbote05LHKot8DbFIbspTYtvP+ucOeT4/HXM5wq2WBVx4PYhT4PmRXsuN6WjnaDT+6no7xidOZiKg0s2gA1xqNPeOrZSPOi6YaIlceDEm4xG18Jg94HKzy4T1Lg/533Ps7GWn1iPDwVZ+KgNCyfokd/4OPIFR7mzWoNNJ7Jk8mNYmactX+DbBHFY4bJi4S+zyGIbaT5G/G7W8rPk/DyI87npew55G0xEnguQCJNRtpKJBZCFTYx974INUFscdG2Piu2tKg6y29/rFId8sRZ+USkIoy+qjl3iydLzfNpu/BwIzz3nmVANL8qF90ckC67tA/7FbywUh3Nje67lC3wWxeG8DXFIDm/JHymXn5dx+VK8i9uc8vntAp/5MyKEvFVdYpWIw391xCH5n/Jyp9JLcCb3HHR9TRdtgDbPHJpobxVxOOqzb9Iw8Uo+TNzrsJOiv7POMwfTxc4H2EgNLvL04/5aPrvJ2xm6PLWQ5WPjzEHn0plVPsf3GNoRqzXwW++GtE4YrWEDTNZhA7SVrdRUe03FQWT+yMJEl2wQXQF27WKlnqixs7aEVkxO/gIofyYizq/nlx0p/d+ykJadIxTxdNnOcMKeM8w4spXKWoHPZ21HZdb4rfu2UtkOXYR4xTZA+NSODbB6iNvWPYem2mtS1CQNE6WHg9JLcGuyQbR3f46+cKrkRYvfvFhLOXljiFsPUTS9WtHOsGfPLdwC1rLnKt1zEJfgXIs627657UIbYAF43OZ12CD1vq176ktdX/FgnEucEDz1zc7I7IuqrxfMN4OuLcIu1nOowm+jeg6eWwDV3lbytM1N9oEN+FRdzcXn2321M8rsi6Z/zzaffYweKleCc+lVVlsWgI9t9rENPI/fdRFO6wk8crP//LXnTBbR+MIp7f3uekVGwWefBELwu+yb1RaAJ0W/i+o5VLY9PC103kQfWNu1eFDe0uWJ7ZOdUcWeE4uXS0kV6l14MPClrPD0OPiU1+zWETOvwuq2v9WnNm/StwOba2eAl/5iUyyAxtJnfWjzY49sEKBdOwO8BNYiDttqAbjcZlt9AMDOqMtLbl9gnDZYHAAAAACIAwAAAABAHAAAAIBV/B9viS4DZH5ZhQAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 9.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
⇒3x + 5 = A(x - 1)(x + 1) + B(x + 1) + C( x – 1)2
⇒3x + 5 = A(x2 - 1) + B(x + 1) + C( x2 + 1 – 2x) …(1)
Substituting x = 1 in equation (1), we get,
B = 4
Equating the coefficients of x2 and x, we get,
A + C = 0
b – 2C = 3
A =
and c = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 10.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
⇒2x – 3 = A(x - 1)(2x + 3) + B(x + 1)(2x + 3) + C(x+1)( x – 1)
⇒ 2x – 3 = A(2x2 + x – 3) + B(2x2 + 5x + 3) + C(x2 - 1)
⇒2x - 3 = (2A + 2B + C)x2 + (A + 5B)x + (-3A + 3B – C)
Equating the coefficients of x2 and x, we get,
B =
, A =
and C = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
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)
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Question 11.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAATMAAAA8CAYAAAAKeV0/AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAj7SURBVHja7V09bxtHED33cW8bXnZJLy7VpjLo81dpx9RBlRwVgnGAPwAVBkSpE2wrfZzG7uwitYHIf8D6BS7kXyD9BimcI+9Inm6/7naXe+QrHmBISsh3O/dmdmZ3Jjo4OIgAAADaDjwEAAAgZgAAABAzAAAAiJkmuSi6NgssOAAbhJi1DvsJfzgynstZ8GT/IRYdgA1CzFqDw8PtX+Lb0beR8VxMwU83h8ObWHQANggxa5dH5BufENYDsEGI2TJ4xMsOv/vh8c6b32QGVZXLQH4DsGiD/8hsEPYHMVPlKfLQPstTML5xVPW3OzuPuz3GvpIHzX+W9vkzFkVnEYuPtw8Pf4GRAFZssLvxV1mgZu0v/x3sD2J2BWk6WIt7nb9zg2L956/EBsfO7+y86SacDwfp8FcYBuDIBl/D/iBmtTFM47XM00X8Z1XyNU3Wn45+fx6x7kmcDtdgFIBTG9zdvQX7g5g1Dfsry+JFfuN2/A1hPeDbBjP7Y9Ex7A9ipucZh5s3eRT9FJ3xed5nr0SRGwC4tsHC/kpRGwAxqzSkbsQqw3j6Xcz5Owr1caARcCtm7HvZBjP76/XeZvY3GD7Cs4KYTQlVlLSznAVP3lf9XRLHW+l+eiPbas5UNQHApQ2K7A9HMiBmRf7hLu984PHg5fbu7nUyjDSJ73Mev5vNR2Rh/chw6He5p9zg0SfKW1AFivNkCOMAbNpgrxe/zW2wyv4SHn0k+6PjGiP728OzRGQ28nRsWJS8O50f63HyopxYHeco2Nl6kj7Nf0YJWqo4kfdEIhZoaIN7MhtMY/ZSbH8bR7A/iBkAABAzAAAAiBkAAADEDAAAAGIGmC94qfOpCHhWAMQMCBrZEYC5hoHVKF/MBwCIGQAAgG8x092CAO3AIrepAODbvsuGegEsD1zkzPBcgYBwDdtM5MyQMwOQM1sG0J24ZenoSReY4yS9D2MGIGYrRpjuwDVp9RPi8QXqG4/2RQDEbIXIjtuwVA830UHRFXQ8AzGYZnrj78W+LLLtctrvPwk12qV15/30mYkDCpnPKvEz4bZSRrrB2VGTF54ioHLLoFA6HORzGhfx2TSII/T+9VlXipEj07GVNvBZJX77m/yBDrelMVKtqIzFX2yJz3hIRfcklFbbeTddmvLj83OpnVIoxQLV9p9a76i+a0h8ymkN1cu8zPxybtJKe1tIN10giqRs8hmLR/c4pLkBWbToMToLSdCpqENNEWWzHFSCH5qDKiY3ZbM32TnN3qSGjzKbpNbccn78exv5qbgJxSy0RVV5XVmP/+mDEA80abLF9f0MlFtNj4NZXIunbvqAvHanE/0YvxRy/tnRFMF39uEMdDmVBglPBwpTakMiaIvmZ5QWMeSXcxNOhw+ddBZ5DfoPVF5X9p3HD46d29wyU+92n/myNzt3uqqhK5P5jF4Gs7j+rDqRb2YDCjETCb6PZ6fLiQo69xj7PNuJliLP8ezN6pGJV/iVilM+bUOFKn4vkvhewU8w2GXC7VRUeFvYC6HroWgLqeN1ZVGJ7VFy9P/zaRTFbE+FIecRqI/0wKT1uNJBVEXUOvkfV2JW2HfphXHNx4RTdnZwMPxdFM1oOLSzRfAzcYR1+Im4CcVMl3RoXlckwlMhaC5mtKCj5/N6JBav6d+7u5u3+v30iY+QXMcr52LmI6rWEQ4aztFj7Ovs96GKcMaFxceyyNaZmAmekSmf/OXW5VOXU4VTPtXgd2qNX7y+pcvPjoMUR16z3JR3M3VJh+h1RUZa/FzjGIWKz9WrQOzMdbWXvn+P9T5vbvJnKjHzNZ1d53PmcyLsnBK3VB3XPebjSsyqvrsPPjbETKeIZZnfns9jWSp+c9PfK/JqtV+G0Lyu6LvrilkTPm4XmB2RgE2MTU/MHBcBTBxEUbFi3ROZ8JdL9BT1ZjYy8tK65XsjMZv5Oxd8bHGa33moK5Fz/CYRjiG/P8Y2b86vSfeWgp/kIPr00Hr1gfVaRhqi1xW9yPn2U7b1suF1nW0vJ2fozMTMcZpA45maOkjBBfjLKz+TfKaZmE2fkTGfPDpQCIMNTgczCXOdNbXKT1I1lfAzblqgy28qZuN3VC5mBqRD87qiF9mEk4nX1d2C1/VaxfZywretYjaTCzGKFp1vM2u+7HN8DK+z1d1mmty9XSS/utDl51TM7Hvd5OMixcxmzqmp1ypXTIMUM43nRC9w3Ou9Na2QL0TMTPkIqmo2OVUdCJc5QQm/M9f86sCEXz0xM3iZQ/G6SjHT5GT7GEdtsZjcRcsxHPBH+Rkc6WL7EDONdERRNInjrXQ/vZF9L4Mqq3sxM8uZifiYHFkw5ZRFLP3nf87varav3+3wDybplqIKaMKPRMOQX62IzICfk5zZnIpz/i4EryvMmRlwqsvH+iLH7KUgkruUVVF9FQBUEWzmEEYvAh30LF/MT9PBGufJnm0boZcg7kX/Enfy2krBN6j2VfHJIu/R31PhSIePKaexU83W+yokTkHIT5Lns8XPNCKT8ataPyfVzBC9rui763BqyscHjLaZHrp5yNZjLMbsbPaEd35WjiJOXUfJI/6fjo1UXo0RrJ/oCM84LeCOjwkniTO7UB6aVfGriGhs8bPgrKX8rJ8z0/C6w0V4XdEiqqIVG3xCETOfh2ZdXBHztoWviLzbykfA70zEz3dXFR/chGKmWtTJDQGBiifv/Xjdq4UC2TUsWR7MBh+PYnYRynUmF5f3/T3HiruZE6/vI+ntgd/pMvIzv5u5ZEa6TF63btThCrIODaFC1pCgjXxWiV/OrdVdM5ouYlsF2qaguxPP7kko7cP1okn2XdgqSuMUOviFyU0oZiH2M1MRlfUza6tA2xR0V9DpbhoKdJp4tolPE34hDeSxxa3Rf9wmorbbZoeGRQ41STh7H3rUmzXT1Dxi0AY+q8RPl9uyGKlWxZEil2XdajadPNU4QmvB4Jtl4VPFbz1Ot8wi6vhxW6Yz6XJbKSNd5uis6eQpAGg7Vo5wNgTYc+9+51FRsv4UQ4ABiNkKkqYDsm3ZQmiF4TNn5AAAYgYAAAAxAwAAgJgBAABAzAAAAAj/A0lC3xD3IFJDAAAAAElFTkSuQmCC)
Let ![](data:image/png;base64,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)
⇒ 5x = A(x + 2)(x - 2) + B(x + 1)(x - 2) + C(x+1)( x + 2) …(1)
Substituting x = -1, -2 and 2 respectively in equation (1), we get,
A =
, B =
, and C = ![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 12.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAA0CAYAAADL0WWEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALPSURBVHja7ZoxbtswFIaZPdkbI/TWA1hMblAwRJM1RRzCUw0PhsElATRkkL0ZaE6QKTlA5wJ1TpATdOkJnDMkFZXSbq1IpiSSkphn4F8cQ3z6wvdIPv5oNpshUDkBhDrhxZ8dKYBXUBOKL2NwzwjhJyaiHsDTVCRYj1AxXEEkF/cAr4SmnJxiOrkEeAUVhqM9SvtDqHklUhcjtJR1z8eZt20xNDJIUvMO2MNoPt/1BdykT0+OSfcWIfJ7EEX71uBF0WCfdI9vi8JzvcXRHU9Ohm4X/Yp//2INnprWZRYMCTxAwSIrMNMqM94FQfel4b2V8+q79R4vFuF3Ll4mL55GwRuPz4JDjH/8u38TlAyTBQKzRdX6VvRlqsbjDJ5Mw9Wsik8Pn8bXASck6ovoYx1pZCIe52kr+NF5/J99Qjh4rHr8UumlFIaDTvIyYdjZ/JuJeEyMVwnefD7aZQfowcQ2hBN0t549K72kvsupn0XiMTFeJXjrw3/2A1yuflXicZ62ckBGyDeZKoRPT+uGVyUeZ/BUHeCMfRVT8SFJFcNdkyIvYyIeJ/BUe0lw9lkV5eQhcZ0Rot8jhEcu4ZmKpyg82fBgh+i7hCdX97cWloyagpdHXJz/13KK91OY8BtT59fkSIfITy14BuLRHS+9NcpeWN5dG6lR/TyABwJ4AA/gvUN4mwdmUFp58J5B+YK0bXvN0+mnAbysvhxGi9dUiA/eYdgBeJqSdw+bh/w23vnWHsCr6yB4dHUF6Rc8x/e33s08ZVWzvTh5B092h23WOx3PSSvhyUan6buRzefreE5aBe+vXeMK08mVulOlVHyxNd62u4hGwdvmKUnfqeKlTU9za+DZ9rh4C8+Fx8X7tLXpcdFpFbUangOPS0p55spWwVPbBBsBe5+2Nj0u3sJz4XHxEp4rj0tR6XhOmgHPgcel/NapvPm8sY2BNgsgALx69Ad6LuyRV6k8kAAAAABJRU5ErkJggg==)
Dividing (x3 + x + 1) by x2 -1, we get,
![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
Now, 2x + 1 = A(x – 1) + B(x + 1) …(1)
Substituting x = 1 and -1 in equation (1), we get,
A =
and B = ![](data:image/png;base64,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)
Thus,![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 13.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ 2 = A(1 – x2) + (Bx + C)(1 – x)
⇒ 2 = A + Ax2 + Bx – Bx2 + C – Cx
On comparing the coefficients of x2, x and constant term, we get,
A – B = 0
B – C = 0
A + C = 0
On solving these equations, we get,
A = 1, B =1 and C = 1
Thus,
![](data:image/png;base64,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)
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)
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Question 14.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
⇒ 3x -1 = A(x + 2) + B
Equating the coefficients of x and constant term, we get,
A = 3
2A + B = -1
B = -7
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 15.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXsAAAA8CAYAAACHFBprAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAoCSURBVHja7V09c9Q4GDbU0B8cSsfVx2rT3jWM4xAoA2w8aQiTYifjmSPMbMEcG7rMTfIHoCBcc3Az1DcH/AH4A1DAHyD8hAu5lW05Xq8/pLVkyd6neJqMN/bz6tUjva+kV86TJ08cAAAAoNuAEQAAACD2AAAAAMQeAAAAgNgnL3GccwwwuKVOgPYB4I8Q+7qNtjNw11bo0jPHoV82x+NLMLpdnQrtA1joj09DfxyNLsMuLRH7wCMPlpacT5NG/A4xsQ9oH8BCf/yY+CPEvj1iz7FBnRcQE3uB9gFsgk+dI4g9xB5A+wAQewBiD6B9AIg9ALEH0D4AxB5iDzGB2KN9AIg9xB5iArEHAIg9xB5iArEHAIg9xB5iArEHAIg9xB6A2ANAxh8h9u0S+9Fo+6LXd16zxrs+fNRDzQu7gPYBLPZHCn9sidjv+fRmdPQ5BeofwfB2IG6fE7QPYIU/btK1WX8cHEHwWzKzBwAAACD2AAAAAMQeAAAAgNgDAAAAiy32/LYbEcARAPgNALFvKaKDGZmdQDkgXvAAjgBk/Oak0m/cnV3YC4DYAwAAAPaKvUwIaxNMh/MA/AZ+A9ju41lH/d5G6Mi9ttUWgHG/OYFtAYtwXksax6aFK+TsAeTsAUBTzn7HJQ+73AkC37sxCMZX2/r948C75vnBjUXhzPli5wzQ5X69t+v9LOLnyl44Gm1epo7zpatiz+rIUH/vpopcrlHH9pa36GB8a1E4y/AFFg9d69dl36Ew/KXj1VVy0EWxfzS83iPUP5h/INy+6BHnbZQeMFu6dX9/+8IqIS9ZhctF4CzKV2v4bHlkIft9XeHDIj/m4/PyiXzLecN9fH00+tHmfq0uXB6Mf9lxyW4XxX6DkkMvGF+rM+ry34c54Sveu+39/QsmZzMO3XixKJw5XxMixd4ZuO5tW9MErO9SN7gvapsu8dHi46PRRWP9mlUNLfFzJSOKS93fWUfWLfYmwqVwhku8V6qEKpxNOL0PJi8KGY83L/Uc8qFoFtA1zlV8dfori3jrCEpTIkHoxmFlzrd1fE7PlfokWX2pSpwjH6fvTUbtzM+pQ96zewC0iP144P3KL72IF2gfqhbk8H8P3LUVuvSs6RuV2K05KgewqEHoG9O3QoUzkYLZfRc5l/HVhXDy05LdXoFHHlT13S7x4T6uSqsSHzd8uxb38zxetWf1cV5W63ZG1nBLS86n6P83J/ZRAzpf6izg5M0Alr1gS/eMssqJo4tLZm3ZVc4J34Y6YxgdsZmeRVc9ltkoNSvsdZ1P7OOfO9mvwwtg6Oc8P1c/k9GYxmn6rtRIIMg3VWFrGAZ73pau3LVMBBSFnc63rMO3mPPTMs5FfLX6asORRF0blc0KreZTMIAX8Yl9/FhVWi/28Xs6fZxtD63im/Lz47wdaIWjR3oUEd1eFIZOGsO8psWeDV6q3henuXa52OhYe5CJgPgMPjs428JZ9FlRzkV8tUSEDQ0skjb6WGWjougnEZCGBkppPgXiF/OZmeUmPq4gyguFePI9zDbzrCmKPD8U5JuOWvJSWLmjwuSh0xDEexuMB1fZj+O/fTfZ4E2KfZiiuuK8U/G+zHrGeXYmwXWD2ybtxMUvPVuzhXO0oNp7K/MNVZzz+OqdJKiLjhqzUcGssAk+8yA67Vwsfnl8zlLP9cWe+fgwymYkPu55wbpMG8rk+av4psXe6W38WSr208ZwTvkm/fGA3mJhj+zpyzaLfSIOAlsGsyN6NhKaPYI/saXGjiNip0TYU/xs4axDyPL4mvbTKhsaGhA/ZwdEmX5Xh5NysU/x4e9P/ia4TbKMz8Quz7M+LpMa0iH2iX7n8CsfHSajuev7d/qk/5eqsL5OkSkbxX44XO/1CfmHd5BoHzK9H0ZIk8jIxN5yKbFPPaeA81cVnLWKvWb/ER1U0jbkPs/2bYvaUPuAGAtF3t8qOcWzyhlOivegV4lfnvDJiH05n5XafLSKfc5zVXnHY5XhW93iZI2KfZx3LQv7o5xgMqp/Y6M624ds+sCJnNifta8Q53C1n89mEs6PVXLWK/b60ytVA6YKG2ofEGOhEJ0ANOEXc4t9mg/XtYpDdjl8qA4/1yf2URsIiX3kHOQwrvD30IYcnW1izxH4y3fDZ0nvgwohaSICmlfsU5zvqOKc5cRyn0zI2PFzlgsVSQVYI/byNjwWsaEpG6XFUYS/KCcV9w6Ii/2Z8ImKfR6furt36rahNrHntVF8jzzm+XuIfb3QXTICOtEZAdUV+6kQuSbnAr6nM5ypf9QlsZexoSkbyYpjWc44jYGCUtJNiL0oH0H9ei7WhoPcb9Mi9mzE4Xn6sh8vhNgLipnKLYvG0ziGObc6jTOvDSV3hjRlo0QcJcRO5dZGNWmcHLG3gI/xNE5UrZD8nX4wOj03cWBW2W346CcTAhZ+V995zb6Bl2fQKvYSO1PYs16//0eTh3bUib38Au0MZ8VRX5sXaKcWADXasCkbye5eSXE61p0NmCtnbxEf4wu0Z4uo0Va51N77JMxoWtCmF0Krw1UVqErNTG0z9LytYC/4IXw+tUOlFWKf4mcL5zZvvaxKzZTZUGaLYi0blYljnk9UpDEynO6FnNhvJDlpE/vs7iJL+Fix9RKongmGod2k8dkxZh7yhp1pYmS2ZYtS/7HNEVDhoSo+KxDkzEu7quQsK2QinJs8VFXWKVXZsKaNqIyNqkSmKb+Yk8/UPnuRQ1XsRCz7DSvJMM1nJeGjQvBlxJ7xXQn59gr5FnGG2Mvk6nI6VOgQk+hn2Q/upCMQFgWxhW0T++vjCOhEJAKap1xCzPnrhPPd5J2snKzjfFXJWaZK5vQWuWLOTZZL4PWF8ta4VNlQi40KyiJEvy8+MNSUX5TzGRxlxa2IT/S9xWI/LOUzOFRWFjlqw3+rxD7m+5/IIm6qXMIuxH6OTmt7/e65HK2hQmi289XyLl5VsWXXISa1ZPIrobaXT0ZMqwavDvi5WCE0YHY2aEsBKA0dobjEccfubS0SMq2pHEuqRIoiqmyZHwmWVcS0nc/MjL+lg1edAQ5i39FOq6pjLwpffTMsszcXyU9syPuiiK5rfNo4eInr1WxKC2Iv2mkVXtFnA6JFKvKqtGN3iHMVX12Ib0vabYOgiNxC1UY+Rd+6t+v9rPJaQlv8nF06XuTnEHTB0bJLIR8/Hb0onMPBq4KvPt8hB7anAcNLugV3zLSJT9Wg1LV+zf1c24XjizO778YsICrNSg6rZrld4Rxdkk0OTC44B563bro4Xlk7y16n1xU+XZrdi/g5xFwQbOGDusH9tvNgRdtEZ2Zd4CzDF1jAfr1J15iPtz13zwq2Vfk5GlzKoN4NW2c0wrOe1LmArnOehy+wePjN91bb3K9ZhML8vGrAQmMDAAAsAGAEAAAAiD0AAAAAsQcAAABagf8B3YAeG5COWigAAAAASUVORK5CYII=)
Let ![](data:image/png;base64,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)
1 = A(x-1)(x2+1) + B(x+1)(x2+1) + (Cx + D)(x2 - 1)
1 = A(x3 + x – x2 -1) + B(x3 + x + x2 + 1) + Cx3 + Dx2 - Cx - D
1 = (A + B + C)x3 + (-A + B + D)x2 + (A + B - C)x + (-A + B - D)
Equating the coefficients of x3, x2, x and constant term, we get,
(A + B + C) = 0
(-A + B + C) = 0
(A + B - C) = 0
(-A + B - D) = 0
On solving these equations, we get,
A = ![](data:image/png;base64,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)
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYwAAABICAYAAADlN8JcAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA4LSURBVHja7Z3PbxTJFccLrgu5ZA8LoUbKKiTS5rJMzWhvgcNq3AY2Ny+0W74srA8jq6NdI80BQZublTV7Dr5gclmItMcQBcgfYP6BJVqjSJtVDjb/giFT1V3tnnH/qO7prq7u+R6+EsID7nmv632q3ntVRe7du0cgCIIgKEswAgRBEARgQBAEQQAGFOdMQk5wwRYQhPENYECJL9JwuNTtUfqUELa34nlnYBcIapeWGXlIKNsd2GtX6gIHHNGKF4ne5y+S5biXYQ8Iaq82XPcDh9GtE9R6vrS6+gsAA8r3AjnsKqXWk9XNzVOwBwTNh1yLfk0Ha+u6VxowfvOXqY+Ys3EVtoCg+ZHnWhcoXXy8OhqdBjAgJW1urp6yKH1iud4F2AOC5ggY3soZRtizldHoLIABKQNjocO2UeSGoPkb+4uUPv50eLsLYEAABgRBAAYEYEAQBGBAmuV5V39NyS//c8nzPoI9IGjexv57/+2v3bkEYEAABgRBAAYEYEAQBGAUfwicgTRXwIC/YTfYF8Ao5KA1e3BlgXW2CWGvUbxtNzDgb9jNVPu6jnU5tK/mvQ0AhqL49vZOh7waO+wdBkL7gQF/z2y3t7BbZfb9IbQvgGEmMKT48RYYCO0HBvwNu5ksh5EdAAPAADAQ+AAMCMAAMAAMAAPAgAAMAAMCMCDYDcBoBjB0tphhIBTzQZ3AkM+mIvgb4wTAaDEwbg8/7XYpecmNZ7veeQwE/VLxQZ3A8AcX7ypJF7/kBf7GOAEwWgwM/8XkA54e6LhrAQOhmA/4mfhd0n3eNLvB37AbgDErMAy5D0M8SGdhW+eVnxgIxXwAYAAYEIABYNSstPw7gIHAV7vdGhDQAIxmACNvrDv+IPyuWNJ9qWswj0arp60e+Z47ip/tXvdZLhsOuxrk398RtvyolpdB0QdBHvPnT1zvYlMGpWn+ht2gGPsy0+1bRg1jY4VdGX/PQxnrVL5zQrCi/9ZRu4gE5yMxZ6d2ZwgbkDfM2bha3+/P9kHTgGGqv42329HAht202dd+ZDI0yip6B7HugNneZzOsMPQAw+zAVl/KpK3AMFWYrUNNU1nACGLdnmpqC8CIkcgVn7Ne6KzjABh1Dbxm1oEgAKMMYIi6DbWer45Gp2cARn3pmLpmmFJ+MYm8lvsH4gpCVRfEVX0AYAAY0FwD46e8wIiJdXs81iUVv6f/bq6BIe8ZYJTs8rxlhy1sr9l9mxD6hs/uh8Olbo/Sf8jitzg3f8Bu8pyfoHLMCmSWHdD5gYFgB2BA8yqH0S3eAKEa6/idH0GsO4zEugP+f4Sxrrv8V0LeifjkWv0b4zi0T+hCuAKZW2DwrohlRu+LjXGOe5n/nev0r/PvztNR/M9HRTD6hhvVYczL2vk+yw7ovD7gu8EpXXxcV+oMwICg+sTv8ZCrg6xYZ/uxbn9gr10JYt01MfE9inWHkVjHxrHublysm1tg+D3tk7uop9NRExCh3Ze66joqPuAvwSKlj+cpdVjWqjKq0WjlrADGaHRWdQUIlbuihopPdnqdzt+z2qxtMYn1VxJTsW4vCpwQIuNYl7RyyRWs8rwcJunYd7TZZ7z3ePo7ihn7VLF5c3P1lHWOvNBZBM/ygYAY7T2VK6MyBnNbpbgCfKfa7gt7xtrzsMiKGu/n7KD1XPs8h0bfcr6KK1zLVvbptlkeYzqk8yoKBh7rFil5JmJdQhE8IVjFd+iopFpMVPQ7hACIqUEkdUetDei6aptteTWMeB/wvGXfca8rbbJpqL+q8n0ZKSmV4NhylbZSgC3LsbkoYI9jRo/2vou2x4pYR8nzuC4oseqIAQNPc/E226XR6FczA6MVy7iE2TsnsUg9Te3u5gHF6vX+rJqmK6+GEe8D/hLIFYZqwQtCDQNqp/wd6p0HlDlbq6uT73DSprwg1h1M7+6OxLqDC/adP8aBKmEA0Ury9SbkMoMl2kQ6StC513sgoRB9Tseybrgb7gdiVRLplqo+iKX7QOQvKQU0AAxoTuWnkJLrmMEO9ol0VBDr/iJBMhXrvhCxjq9KApgca7PVCYy1Ab2VNrPWucIYP8etsNVs4N6UaafBYPCnXo8+5gbjP5N2kOkq17UvMObcrRsYIfxqOu8KwIBMER+ns9zbY0JhfmPd+pjXJPM8gz/+nZ2kf8P/T94WSwfDcaz720lup77l3ghi3V4Q677jMYRvL5DxxmHk4YlzCy94qy2PdYn7MPgPOLUWOmy77AEU14FUl3gdQKSGKNsNW2pF7o4eWLb3B/lnXiuYXsaJpV+Fxe88PtAR7Py9J4PPdVykNcskgEO/yIAPT/3UBIy227OOjMEsnYJhnl/UU9jrpNy9FvBZ/Rty1q8Wx8hO1ndfZvQb8d0isW7ox7f9cay7GMS6/b69Zsvfy1cmAjTMvj9d4zgW0JnjfDlggztlB0W+h2FxkW6ZAAyTZ7t5fFAV3KPBjfutCfUsAXS2fN/kINcoe/KgYbg9RbZgPIGb5Rl5kI7MrHfSOoR0pZhU0sx5PlvqO3yctOXfsscdy2fufCkEYKjMdtR84H+ePqkqADXNX3Ijk6nP11R7mgoNvvG2zHffT1ez3TrvwxB1B4WjxmsHRpVBUM6WdQyYedokNAswsmzk70nRdy9KGf6VtZ+6GgGyW6WbZ09G6K6JjRXCnvyUgxJXA3XdYlfE5q0FhmdbF+VOxKDofauKgC7PhVpgne15uc2tKDB8GKS3CYsiv0EFdVX/irRCDc+dZdOm21PXJEx1rxK3Z9mTTw4hXhSue0KrYvNWAiNSUJrcg2C5X1exfO50yCt/1y6AkfpveItwzE73ydmwnuNhVANRxL9v0/wb3mWicZaYZVMTj9sx0Z78MDyxF0qMYfqGdpe/jVtByGMtyrSnqC9Z1hdVNbTIjswQ0Cn29Nth0++oaO0KY+KF0JCSmqf7ooscbx5u2kkBht9255/YW/XyO2+XV5Z/w+CseINYGcqyqS57VjFe8t7INosNY49sOWf9axoa/mcnz0aaOZiPAVoUQCqTnqEP6B9CQKfAQMXmZd2HoQUYcctGlWWkKKJVsLqYX2DkC7j8oD1xfMAKu5kGjCwbFvW/FmAEnWa60j8qNtVlz0qAEczmq0xLydlytI39K8daDCE8FTjDo3pKWPUEqfL1IFV+kvtzMHA/z/MO56l7+CdBZADj6GDAW+n1Jf31lkJ5PulIIWo9dz37vHipgkPc6lx6AxhptqH3uW/idrsfS68kHLZ4zP98M2NB/1cBDN2HRWbZVKc9qxgvYVq5wnZT2UWZtOqIfv+jNHdy0M0DYPvY4Yn5Vi5VAiMN0o0BxqTTjugvl4lZJ6gCGPWkpPx9Cs5WZCDG59vlDD0l4Jbl/0qBoeEdULFpEXvyIKFrPCkDQ3NdKLKSmMjlh8E0AWABgPdjAPxjFQCuAhgqkG5USmrCcYS+GTjONbEsL2GAznraK4AR76uof1KBEdQAslI6Rfxfxl0U6sCotmagalOd9ixyMrI6MPxLxHRP/qZrnlnAOEpxkWfcH/IQvQDA+2UDuFJgpHyuccCYGAwlDk7l014TaiEARvxMLRrIygDGZDpFLZjMeheFScBQtWkN9sx1MrKpwEjaRBfaKKOmEoDlxwkAl1TziJv08CNFVCCdDxjJNm8kMGQON3gpb5kQRAGMmIHXXf524vJ3eYFUzLk1YYBTrAHM4v9qU1LVAcM/kkIcm3Eyy6az2FPH3oc8wNDV5SWL4HG/TxUYRQCsaK+HMfd4xEx67EfJF07NKTDEZiXmbDkWvRvXzQBg1A8M/3Cx2JnnO1nki7umViXAzer/ptYwApseqth0IoWSYU95NlJgz7c6xpNpNQz/cEZ2M2OP0IFq15Y8aLQqAFebkmoRMMJ2wvGLVmeeE8DItw8jKyWl2mVUhv/b0CWVZVOd9pxpvCQEMN32jGu9j1mxHah0bU0DOOlSIACjYmCIW54ofRL9MvJoBHFE8PD2b+sIoP7tU+R7/gxZF6MDGMX3YZTl//z7SLL9q3sfhopNwyBR2J6j39U1XqItnlpWFoO1L6OpPvGMnd4DaTuVovcEgMeBeSoAs+YAoyVF76Nim7/0jvSSh8tz3XsxYneKphRPAYxkHwUdJYk567L8n+cuiuCZD7P8W9cxHMHtZodxv7egPferHE/yeRXteVClPeXmubAVdlqR9JNKy2kKgA8kgMuaTOYBxhSgWdIztLKtFmouMNQGAXltQk2q2MSB7ZmUkgzPPoI9E9NQCTWht0U27h1txvM34VUJ4AAY/8wCRjyg4wvjahv3AAzIEGCEs94GXv/qnwpr3soS9iwbMPo3EuqeYKTdRQJgQEYBw4TLZIoNNLpr4iF/sGeJqx4xWy/v8EEz35UWHT4ItR8YcibXpBvixCFyFR9uWYY9m9KMYao9m5ziUwKiTAOmnjcFYECGAYOL97GbdI9D2qyMMeeu6c8Je5ZlR70XO+n/bs5O+k52AAMyEBj+zNhasl3vvMnBreqb0mBP856x7CtaTVDaLncAA2oEMCDI1Jl429JScrNh5rEnAAYEYEDQfK8yeMpSpcnA8y599D55/+dLnvd7AANSBMbKmfOE/O83jrcEe0DzKN4xxQbuzTbUMlynf1358jH3k4vvEfqTdfv2hwAGlHOWZT1pWy4XglTFr3M1uSakBL516+O+415TAR//zNC/VlZ7xx1euBZItGvS3tOl4bD152dB0LxKnLfl2hesXucBvxq7jkkiHNEWaIxfpB6lT007FgOCoHIk7uKgbLfOa7DhCAiCIAjAgCAIggAMCIIgSLP+D2cAXM8amxdyAAAAAElFTkSuQmCC)
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Question 16.Integrate the rational functions.
[Hint: multiply numerator and denominator by xn-1 and put xn=t]
Answer:![](data:image/png;base64,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)
Multiplying numerator and denominator by xn-1, we get,
![](data:image/png;base64,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)
Let xn = t
xn-1dx = dt
Therefore,
![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
1 = A(1+t) + Bt ...(1)
Substituting t = 0, -1 in equation (1), we get,
A =1 and B = -1
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAABDCAYAAACCwoCdAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAs2SURBVHja7Z3NjxTHFcBrkXzCRJG8B7CpkRyZQ4gihakZ+US8h9VsrxeOYzPbmhPOHkarTmCRRhHBPdxQhH2OyQHsS+CQ5GSSAH8Ayz8QRyzKIbYi2VySnL1kXvX0bG9vf7zqz6qed3gCiWW26tWbX72Pqlfs5s2bjISEhERVSAkkJCQEDxISEoIHySIYH2NLUzlGusinP/iT4EGyMEY/GvXbHc4fMiaeD133FOlFXTYFu8u42O0NtjfqgDAtAknl4NgU/JOp0T+1bOd90kk+mTjOSVvw20vcerw1Hp8geJA0VtyBuMj5+v2tW7deJ30UJ47Fr/Le9g7Bg6TJrvbnwp5cIF0UDGXHOse59aBK74MUT1KdgbsX3ubs+NfvOu57pI+idbtydpktf7Piuj8heJA0FB5v/HNq4GdJH+aDmRRPQvAgeCwWPGY1bjonYJBesfAweW3rGjvBQ2GBtge9jTXR+j1j4gWdEzBDrxh4mLy2dY6d4IEUKEu1Wuzv08XaJ3iYo1cMPExe2zrHTvBQFCj7ETzM0atKzsPkta1j7AQPggfBg+BB8CB4kF4JHgQPWiSCB8GD4EHwICF4EDxKhsesT4DWdXaChz56xdgLwWMB4HF9tNpuc/YMFDBw3DO0SASPJMHaC8FjAeDhTZ59zxj/1nLcc7RIBI/0n0+3F4JHw+HhusNTorV2x4R+CwSP+vWqYi8LB4/x+M2q4dHdvrFC8EiOr5e2tvo/sAT7EyzS6ui6qKuPYxFz8fMFdc8hi17V4LH64x+y1/7zo213PXUMHfZH09a2zrF7uj32Xz50L1Vli0cHAU1FWPuZzsSfDMWG5yYHRNj3TIRHYC6v6p5DtF4HiWNSsReMa51lDHrbZTVjLyJsOWyLm59nhAf/h865jqaJp3P20sQOWyr2Qs2A9M95zGzxu7AtRnkiBA8dFn4gLpoa3xM8mgWPiS0uTG1xL2iL4/HWiZ7o3QiHpgQPDUQm2KD7tYFNgTPA418Ej9LgkVu3YVuUz2T0+DVuOVeRnoeZLrQJEk5KyYQjYy/8ztd+M5mIn18yPeSCubZZ+zFVx8oReIJhdXS9XYQt+snfTev0hDH+Mir5S/CoGBzQLEZwtguJqZZYu7M96A5gcWDnHo36osP5X1h78wv/5x2re3m6Ht/GeSYhA0iSpbrhAYfJ6NmF8mT2/MI1VKUk3ha/A1ucDK3z0u4geSr7k7DveW+0Q/CoQSBu3GzzT+VBqtljR47d/RB0DWCAv88y3fsz0rdtIT5OO+FrC3bvSIY/QqLczqrgAYYK81/n/L4YTjbIHsoKXYanOq3Wl2A7SQCRtggPb0XZ4mnriQ/3sFdMYUtNHsdmm33hUz242OHFOQBK+5kJeac0e5Hek9291Gp1viz6hbi6vS4912NwBgDStewrUW+4gC4G8hBbpC3uBW3RS54e/rlc8EAu1kLLEZ3KagrbD+tUuvGhZOOtW1uvW5w9Du4AJUIt/9xS7AXi8K7tXMJcslT93YMcXlfTbCwMCLCtDu/8IZxfSrLFFmt9FbTFtER+DDzis+eYxVp0CepLwuA0exJehLk3EgGJ7R7fwZZu8+y+eeeGsReYv/SmeOdhWjJP9XfnBKfpdrYUF5JYndZnXNi3HWdyEm2LAAqFkCUTPIp0OZsQjmR16+WbrRCehE6VjsfDN61O57fy/wzci+kZdh1yHun2IuNxzh+qVANI1MTzWvmDOC8wzhYhPPFs8eBUaVrIEg0PWU7jpcbbXhxsva/zdX/MlwZi+DSAeIvAXvkLJkti0//b6XQ+8xcy8NbHkm1Zl52Jc1LuELPF1Bm0KvYidYE49kySTTz9xl9xmNnivr8pBWzxd/5m5dvaPGQZj0/E2V8t8IBdtwlZdyijpnkH/nHfWQntGECzazmX/dCk1+v9stPh96E8C//m6116FFM3cjTqt4WwP9YZHoLxXdwhMb3PeegGadXxpD0iPtmxfubZ4ijWFmEdA8nTawCcuO/qkSQSxExrLXGnrAWWScJpPNYUNxHKj2muOCQNZfjAxVPLvrLugYdflaWygftz/+9d2/lwvtBDsQF1dtCVruciVO0F9FWmbeX2hnu9D3TxhmHTET3nIyxA/JAlDeKDA1vc9atfo4Ater97cGYKj+eQp0qqkIV2EPZC2PYvLGH9piyDhfpyk46+L6ornsVesAZeBzhsIVzdxiU3ELH5yTTqXdJRt6Ffzh6X2T3MO2FoPcgLpmD1oO46vh/mLVoi0PO62CMVe9H1Ytx23N0NDd7MxZ4abXz3dIjJkko/CjveHuQDHHfqXsHx2grORCSHJeweJQLLgUfZG4N31kbshkOpOt6djZqrn1NK25y06CRWvpub/+SqLHNatju0hn3HWT1fVvMi7M4zu8ZM7RBTbUB2u/oftttV3FXwoje0qApFnndnswAvaa7+5pT0uaq6NQoes7rxyyJCIsib+IlEeWKuhA5cKjsPHekvHh5S/zHhRGHjQaybai/VLBWltLnON6eEnqhFtCHUFh6gnCJ253ApOa08lXVXUNl5MKfxdJe4/pVF3g/Bhi1pV8ELtMmdtA2tbHhg5jrv7pVwLKCxOY/5sdgi4BHwNFT7rWbZFTDG48PD5LxH4KTqK7+fgywXyivbHHXatQh4RF4FL8n7wKxtmfDAznWe50uwLyPhgWleM/9yIRKbaZ8HRu4fWpENW7l4iq3NlwWPORxrTtwW48Z7R83BVe5a9q9kUrogMGINvApPDrtmZXsemLkeGmvETVnj4CHbk436QnD+10PNa3rio3DzGgw8VD4vX8hTIjwMT5rK0BKqWM7qef8wm58XKOKLjIaHvPmZfK8i/1hwG1ra+ocvJo7H/bfAxvrj8VuYtgCYuR6yr5i8h1HwCLRpT21e4xtg0u6l8nn6wqOYhHAd4s8BOkpZltNXyQsUDY8qerpibBKz/tN/vxtxEXEf+wQDZq4Y+zIybME0r8EuFPbzMiYB/V3hCXZXWCR4zNcoYMhxV7jLhEdVyeei4JFng8LOtbHwwDSvUYFHkc1wYq6r76s8GLUo8PCqYWw/eAmqyJAFDY8KQpZDNlljzgM718bC48C1jVcwdqGwn0dhS0nJwxBEPaB4IWRV8MBcBS8w57GHhgfy3VkVG8POFZNTMxIemOY1KtUW1WY4esHD5IebDh+WCmb4ocdIEfNKM/CAG594FbxQYMbYZNZ3Z7E2pjJXTGXIGHioNq/BLFQVzXCoVBstXrJaPA/OcWbcz1VK4bnhgbwKXpR4YW302mZ9d9bTm/hbKjwU5npwjig+vDYGHjKsUGhec3BjN3qhVD+vCniovBjfhENilXg4mt2q9QChf6gZ936skfDI0rwmKY9RVTOc2a7wCHf6L2rniSZ/E46nLyI8/LxH0eFx4ZCLeD+2ETkPNQWYW41QzRmQ6A+PuYeruccYd/N3YeAxv5KvOeUzzc175X6PruSbBw8P/GIXW02pWqCAgOkR67orZ5fZ8jcrrnu2cfAwhfJl7Qwk3gbyDmP/fmdw4wOdxjXr1rWjY5d6CPcxFwNd5933jjP+9QXXfbuR8JCUhzaEMZd7TBRd+3LqCo/pLvp0ma/9WTcbgCbVuoWd8lYzolgg74VZb/z6OPvpV1V6v7XEmE0KXZrUDb7SnZ53HvZHo3ad/UGPjsvq69Q9HZ5FSIXGqN+GF+IYX39U9TGBemJMvn6/Cd6H13Wb3yavI8MX1RmcgweZw+dLSJTC5bvecx7ln4nRAh4gUAaFNymM/wLY3UtNeLyKhMQYeIBcsa1105+bDJ5LISEheJCQkJAQPEhISAgeJCQkBA8SEhLz5f9LJS7+WN/o2AAAAABJRU5ErkJggg==)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJUAAAA8CAYAAABvsfhpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAahSURBVHja7Zw9b9tGGMcfpWua2XF02mLP5lljNkO61Ek3IiAJLXGigRAOjROAg9BQ3owiyQdIB8cePXQL2sbO1MX1FwiK1F/A9kfwS3l8ESmKlCjpyNLKMzzwmwDr7n68//OmB7a2tgANTabhJqAhVFIXD3AL14FQyT6Ma1wHQoVQIVR4GAgVQpW77wOwfyv+PUKFUE1ltt26SwG+AmEHZlddogT+hio7bG9v30aosi+04j2N5Y2wij4MW6OPCTPsFmupnK89IKAct2z7LkKVEaiO1lhv0tqvAPRExsbNA1S6Qt4RarwRt5MADKjxAeUvo3FGNms1+OJcVVcIVSh/CpBjxu0V8dDpFHap0XuEUE36ZDobh1CF0hfcTDZnK7KkD6GaY6ji0VzoU3q/c/Zih7Z66+L7XouuA6FHGrfvI1QIVaL/aJoqpYT8AYq+58NU4ay+QQBOgTQ/yYjwEKpvCCr31gG4cOwSgJyvmV1qUPpa1i2EUH3D8seN+hPnZjoDorjO+DxHsQhVQYexvd2+zQgcyEpoIlQIlWudBnnprteyFhEqhGpms6zWIltd/UVIINXsxwgVQjV15CdSBuKrwdhT3uMLrAqHQPXdIApEqOQtstJuq3cYhd8EVCIiylqR3/frhUXUDGc9DFfuFH2PG+yHwDk3KHyAavPQNFWFUuM1QiXJ/DD7csCovpPxdtsJwvO8o6hZD8NkZNN5n6d1gz+Jrl3kpwjV3hTlsBcBVbRBIP7Qx2/k0kmSMLekAfTfvGUTm/Syq05Hq2uEkL/6OTlCj1TTWu6aa5Q2+LPSQ6UrsCergo9QDbzu1qRAdTSqE6iceWUl3lcOm2v33f4w53/HC+Plu6W8ZrYTWRV8hCrcVwWUg6y3v1t+apBXzperNCn33JxhRblR0hfX9YzaX0GoJofKOwe4HqUY7gVQa76PA5cYdY2xXMPkJOkT/9Nqtxd1St4Gjn+FKMeq2V2Kvk5ov8boplvI9Zz9U9roPE977wjVaLVw9u9sVLDkvi4hwk2IukYbYXyzaOn7WVv5Ueh60DWZVBKxrPb3jSp8FiAx48VDT/dF3xKciys86b0jVNPfUoWnFGRKnxNdKC4YsQX2DPoomnbwSiSDTqMLn0hGptTj5hmquPJYlnrPgepQtax7zs/fhX8bzh96SethB7xwqCC7fKb6Q5706btDUCT4WB5EIVRu0jGW2+oDSdjBOKgmff9lsFFQ+cpzEVOaq3H5w3DPp88TSvOpskhn1NKkLypRgXyRRudlIoAR2IKEa+BDWaa67G/OadBxOQaqy5tmecifVKj+b5/Kkz5vIQG4nsQNX8Npksgb9Jnb0+S/11pt9eOoZjn0qZLNu/WdfR9TGE+9YEqV8HRkyi3KMuNp1G9aM7tK8DrhkDf9Gyj+JImsrxON2FnLIwhVsvm3/hVUG5/VdvtOEkxCRVir96C0UPWlr9F5ZWvaSrDw/qd6qbYrFidSBp4TOQyUL5VnRNHftdvWYpaiNEKVbl5dU5RjROrGWg6ce5HaEe3SdcY3Sh399VP+pPkpLlcCFkrgKMg7ibQC572F+JPTNdWl1Vrt44BUk9XfVdOkI/zAWVtfcpmNkBdUFOifk9RTXxjsob+nF1lditKlFKbc0EqnQZ9Hn5we5wuiv0nAKD7QmhYazwJVnrMR8oCq0Pdz06Hy/K7kFl7hf4lIJg+oguAij9kISQ/OmNIUQiUVKj+VQKj+Vvhd/WSf0H5GbHFdpx30rIeR12yEoZt4zFwKhCoHi2h/mP6o1b7UmfHTKDmaVf5mmY2QtQ3FzDCXAqG6YVHTKOmbdjbCpJGYeyuO6Pefe6j2U7LvRXU5yIIqz9kICNWkfkaYmb8W2Xcv3F9TvLQAOS/640uTQhWfjRD8TuZsBIRqCvPKKOQf4W+I6Ez4Ntx2c1En0YJxGaEa/NCGl82XPRsBoZrCOqINtcoORZgd9DYF9bo8+7Fkyp8/G+FcxmyEWdpQEKqtsMpdo833jHF1ALQCPnYlCyqZsxGmbUNBqAakb7CHqd9OkdLXVNborz8bQXJCE+VvGumDylW0h6mM0jfuMCKzEaQHFwjVFNIXzyyXUfqSDiM2G2EjOhsh+DtCVTBUQadmWp+4KPKWaVhH/DCKmo0wCVRZ5lLMNVT+hwu/RjcrrObLG5yaF1R85GwEQ9pshEnaUAbHPyY79FimuSE+Fa4DoUKoECo8DIQKocJ1IFQIFUKFh4FQzRFUl3OyjguECm2+H1bcBDSECq309h891KWKnmthLwAAAABJRU5ErkJggg==)
Question 17.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Let sinx = t
cosx dx = dt
Therefore,
![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
1 = A(2 – t) + B (1 – t) …(1)
Substituting t = 2 and then t = 1 in equation (1), we get,
Therefore,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 18.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Now, ![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
4x2 + 10 = (Ax + B)(x2 + 4) + (Cx + D)(x2 + 3)
⇒ 4x2 + 10 = Ax3 + 4Ax + Bx2 + 4B + Cx3 + 3Cx + Dx2 + 3D
⇒ 4x2 + 10 = (A+C)x3 + (B + D)x2 + (4A + 3C)x + (4B + 3D)
Equating the coefficients of x3, x2, x and constant term, we get,
A + C = 0
B + D = 0
4A + 3C = 0
4B + 3 B = 0
On solving these equations, we get,
A = 0, B = -2, C = 0 and D = 6
Therefore,
![](data:image/png;base64,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)
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)
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)
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![](data:image/png;base64,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)
Question 19.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Now, ![](data:image/png;base64,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)
Now, let x2 = t
2xdx = dt
Thus,
…(1)
Let ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAA4CAYAAACFWNbhAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAZxSURBVHja7V27cttGFF25tnvb4bKzU4srtak80MaySyYhMaxiq9BwMBlLMyw0McROhZQ+cWN3SZE2mYlcJoX0BcnY+gLqFyQHiwcNUXgsQCywC57ijGYgkbp3z57de/dxQabTKQEAoBqgEQAAggIACAoAICijnCFkTQDEAjL9JAkQVNhA44G1vcW6bwhhFyPXfYCOoxbugD1n9uEz0+w+Otq5yyk59frMtYdP4U8flG782d89eLzygnI4fdXtkn+DhoGgVGMyGT3sEXrOHXfd2D5jsRdCUNGg4DqDR4HQ6OWT3YMeQj4PQ0beQVDqo4GgnemlyYIaW3TP6ysf433l0GbP/FmLDd9BUBBUbR2x0+n8Y3I7+2Ffh7xfFE4kKGqN9yAoCEo5Dnaf9Cj9+lebU9fkdnYdvk4JuYzngLGZd7bMzAtBAZJ508493t34WbSt384d/n7n6OiuweHeRX8y+cIT0p2D3f7jLdb9RYhp03a+W/lFCQiqniQ+GtFNFtQ83Iut7gkhdfjwcGcyubd0jglBAVKhXm/4kxjN/ZkqIf8wNdwTAnPszW+9ZzN/kFhSVBAUkB/qBfs2V7FRfanEXYdwb7GP2Iy8rcIvCArIaVN6Ek/SXXf0gBFyYaKg5uFeQrgaCA2CgqAUQax6idMQm9z5PitkMi509WxfFM08jPVm32X9aldoskF+F4ISO90407ecmMaDzQGl/Ld4TuE/t9hL/4SBNX5pUhuL/hFtSIf94050ZM1T2bl/9IjZx1iUmM435K5vgNlvIY5yCPOJIGei/FSER7EzcJ9zqfB32vePEdteyAFvrPBRuvHHwHHWKxmM0IEAoMLZHY0A6BZuQlAAUAHECmKP9E5NXlQCkQAEBUGtZigkCwgKggJycGPlLQOUO68gKAgKwKy7FtwE7p1Gp8BNnHVLhxWAOjQdMtblV8qs+0lmT1FXvhaNvAaah4ocSiZcbMKvsiGfDv4k+YXQAzkUcijkUEAbsRKC0i0hLGqPzgktDvCumKAE4Y5lfTNw3EdaNLjD15nlvJDtiLrZv4wvqyIoRthfrRSUINpmzNWt9po4WU7Z8CSvI+pqfxlfgBYIamzR/SYT3KwVK1Epllrj/azP62J/3lK4jC9GdqyW1ZmX5TPxYXCzsXcuuXy5VrXheXXKg1ibnqeVzG3S/nk4R8lZdN9GXMbLzhvSfTEtj2u6zrxiPq8iPlO3J5Ie+jcbJaraiFuQFrN+lLlkJuuobJ3yLBubtF80/ia3f4gu5dmcvvZvuA7c52mf8ZfEG6gi1CR/pviTwud1Gp+JXyBTMyC4Du2FVRJFLcqs3uTVhwhu6d7+fZP2iwYf8VF/8Vle2a00X1SP5E3yZ4I/ZfhMyj328grB+/fzeecwdj9/rW5C0oSji/2LBGTlc3NfMmaxqkfypvkzzZ8bfFJymsZn8Y484F/5RQFjZ67ykn8lggrLWS2OFLrYH42afj7Hhid535/kiwrowp9Sf3JmqeX5TC/mkjia5pXZLVqbTQUhSbbqZL8YNf3KQYT+Zw3G21mjpqzdlXVCDfgzzR9ZPpNHyhxig5g/PaxKO5Y/mkweyi4/Sgsq9je62B/a8XGh0up+rqBq6oBl/S9yraJOQYX+zFT5E/L5QYbPxFg+L/TIKxYfHuS8LnMsv7igPncMnez3iXac+zajx3krXkm+qISk/1cq+TPNn0Q+vQF2aUGVKcWrNOQrKKi67L9NaLpY6hSULvyZ5o8sn8mCylB7XrighaA0sL/I/6xTULrwV1e4p5DPWb6gJHKQMu8GUiuoYjmUavuTYnFRIzyrymqdOZQu/FXuT4HX0Kjks9BqU3x6FSqVLaxelBCZOuVlVvlU2x/NkF229aa/e/DYP+1u86eU0r+zRtC6Vvl04q9if/YV8jkL+Jx8KcNnoZFFvHperF6JWtDcdp4Wc1zuWL5snfIy+1Cq7b9d/5vOxJ6F4xzel+kYqvehauEvqY64ojrzoT8fdOKzkhi7CaSdlDDFfhlfAPOQOlrqTm7qWT5D7JfxBWiBoKbT5k4/F05GU0IJE+yX9QVogaCCEISdJW1c6QCx080IPUsL63S3v4gvQAsEJRDeJNXyPariRHnegU6d7S/qC9ACQQWhEz3WLRfxb08y+7XM3+pof1lfgBYIKhjpeV+nqkeLL1E2yf5lfQFaICgAACAoAICgAMB0/A/SiteqP2F2NQAAAABJRU5ErkJggg==)
1 = A(t + 3) + B(t + 1)……………….(2)
Substituting t = -3 and -1 in (2), we get
A =
and B = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAxCAYAAAC78KvKAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAGESURBVFjD7ZgxTsMwFIZfmCk7Es4d2qeuTFXqKmVEKI2y0QxVZImClKFDkq0TB4ClbEzcgANwAhY4Ab1CC3ZDKqBpWqTYgcqRfiny8r7Ez3/+F0iSBKoUaICdA+CX8ak95QCicOBYdhvNWwB89aLoUCkAo2RomvDMQeaVAGTqIdxpAA2gATRAJQDCin3/9IAiPAiA1mCEYk0ZQOyhzQvOvgndic4DGuB/AGQxagsZUgBchMnKEcoRoWz4p7Zgy7e2lAyA2W+kT4EG2G2AHDMzlAGkc2HTIQBTfv8OQKak0bv2w7CmBCBy8CSdCZdnfr4AOaKPRRClFB+P/f0OIfdNl51laxcu7fC38SYg0I27UgEiRuvUiY5XIpqLXSUA6xRY5JKH05eidCwVQMTzTV9PacVHg1aDAD5tmg2kFA9DvyaakrKortwJhR8wC8/Ri+1KnFA03s99L3LEkotjH62g/9WOxajWNvFmXS+U+eRXqQXnqGA8KwVA/J4rimFF/aDzQOUAHxUE09F/KaU3AAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
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)
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![](data:image/png;base64,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)
Question 20.Integrate the rational functions.
![](data:image/png;base64,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)
Answer:Now, ![](data:image/png;base64,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)
Multiplying numerator and denominator by x3, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, let x4 = t
4x3dx = dt
Thus, ![](data:image/png;base64,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)
Let ![](data:image/png;base64,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)
1 = A(t – 1) + Bt …(1)
Substituting t = 0 and 1 in (1), we get
A = -1 and B = 1
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 21.Integrate the rational functions.
[Hint: Put ex = t]
Answer:Now, ![](data:image/png;base64,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)
Let ex = t
ex dx = dt
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS0AAAA8CAYAAAAzHuxkAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAtASURBVHja7V1Pk9NGFm9zTvacULRu2Vw3avnInii5B8hxirFVvkDi2nK5tMWfLR/YYHOjEthzIAfIXCBUJTe2thKOewD2A8xumHyAMHwE/qxeS23LHsmSLXWrJb/Dr2rKHpju97p//d7r916TmzdvEgQCgagLUAgIBAJJC4FAIJC0EIhNFjghrQAnQjw+gTJB0qpsAaLyUP55MO2zc8F43wZ4T5j3APWGpKVV8KOue67DrO8IYb/1J5OPkUhQ/nkw8flnlJDXzJueX54T6g1JSxl8Tq9YFjkIjox3SFr6Mayx/Cdd9nkw5sP4mMfjwYcuc78a3Lr1AeoNSUspeox8j6SF8l97zJT/IgkKrI+hS69R7l9BvSFpofBx8VfuDs0D7+TEeNw/yQj5jbqjq/DdYLD7hx4/NSWEvj4zvB589b7xLiKSFgofSctQ+cv4DaPkefDzG4t17o26rBcQ1BH3J59N+/w0JeSVCMoLd4m8pXy4FdYWkhYKH0nLMPlDjGrPpv8ICOoV9/yz8JnvtS9AAD7uGk4m/Y+l5YV6Q9JC4ePir8zC2rPJviCswKKSnycRVBiUDy0v1FvDSMvUvA4krbU3dKl6NFH+IRG13i2nNFwfnrEtYv03TlDLQfk66gBJK+FDULZNyX9gkl1/8gmSVj0R6fFFmXo0Tf63bg0+4KfI02UiAutLjPUUf1qla6hCB0haqROELOJFcxtJq44uQbl6NE3+aYmjYH2JeFYsC74K1zDSwZuq91KjSUucRlbnnqlJd0haOTezIj2aJv+px87DbSDrTj6XFhYQmeM43woyCz6Xme8z13A8/lBHNrxJe2mmt/H4JJKWvriAyLHhjPwEwg9zbMwsgDWhSLdsPUr5u4bJf3qV/ykgpyPq/uVvIG/f42fb3L80culVGKfrun8FCyfmGl4DomP96bltIC2pt45DfiTENnbfrLNnUsxt+4Vplkys8HUO1rtvImmZUKRbth6jOb1ZlH/3gQny7jH6jRgbZc+4d3kHPoPyFeGSdSd/DuXR/STYrS8ty3kif0ebDiq0bkzWW8o4gz3T+36VJZwiaPq/bbsS1hVr0fv3UY/VrwHUwZp75iirsB0FrUoBYZFuZbEf1COSVk33zGHcMoWkYc743xduhlHQilwWSHbUnA9UVz1G8YzWut/VhbTODK/buCfyuPnzixKp+6TCduPcmjoitUg3EPb8u3lwMemzprmn68Dn7UvxW764nEbddhcC6xgiaP6esQk5jBe278nC9sHYiRe2o6BLEP7wgnt+VqTr8Luw0WQ+0HC4yxil/yJ2b19aDbBJReEu7fycZIk9jikzA60mbBhIEN2h9CFYJHJOInUhdBdeVuViF9UD7qX0PRMVtj9LK2y3CPm9lVLYjoIugMUi3fBGKl6kCz/Pb27CVigeYzeyMqMDM/n+sRufBKzqUFA3PS4TlySsirPIC+kB91LynukyeiehsP1oubBdWl7HSA8FvflpsbJIN+aHz5Viv9AVY6qjHkF2DnUeeh77klLnn6aVkKF7WHzPdEWSa+KeOcxb2F5I0CS/+Vx7HJOTLNJdSlKEWrPlALioj6Pkl3gdXJUbxjRZxgGuNRQ5ywx3HetPsQ6O0vbS1u6ZdQrbo6B8DtLKd+uUZTY3CcuuTGqRLlhfCeQkM7TzJBqWF9NK1mMel0eXLJcWLwsW7wH3+EVKdx4lLVgV81Ab00rfS1XrQQNaufZMQmF7mmtYmLRWmYF1NmE3tWKSinRDP75/kjvO1+LUzWFBlBfTqk/qSnTaHsjxQnmO4/Cvs4jL/JgWpg8t7Jml9Q8lVSJ0EuwZufeyCtsT4wo2oRvHXsTtmMfP1jEeAYKF4GAWcc2KdCPSihXp3pVkJlMa4DuP84v+1P9InDRRiYJqYi+qR92ERSn997KrDaUdlHm3a5unVSMdqEZUpvMuubC9tVZhe+mCBpbUUYyqCjJnKE+sgrrDa2lFuo5DH0KaA3wnZekx8oCc6jwdDndtxrwbqjcMI/R5HTYM1A6mrRlY7HVdT6p0YBqJ5xlPVNj+Kixsf5xV2H64qrD9WGAQriQ7Fru3SW6MODGDk7HOJ0J09f4oK4u5y+jt1CLd/vS0H/3c9vwLC5YDKI51b6sMyBfVI6I8HXDLuVumDsI8P75riicDZMRc/4s8idLzwnb7mUx3GHF6mRDr93hhu03Ir5bFnsjfSSUteVXPPO/L5VqfNU7MO00whYX7F7hx9T3di+kRUYoODgMdDMrUgQg1MDYxbY+Fbnzvjq6WNwsWRoeSnzftsBjGJXYebaqgx7Fr0jDmU13PH+ki17FmrKgey3YbTH1roI46GFX0wGwePYKXAS6dDte1vLiETfaL9N4Ob2roERCFcK1SSlx0QcSf7N7+lrk0rTL/LyjV6DDru6o7ndYtkJ803jD/jz3PI0elekxJ2ZHxO6j6qAVpzV2SYpm/QFZQhyT92ypP//CGcHvaOkP8xWXuV2UdFHDyWhY5aInaserkWPa8qhqvuFHL0VBSuR5X5BnKg171IVFeDIjQ10VNYXErR/kPqhbYOqf/NpVgpLUAKcUCr7CnvMp56RxvaGVlr0UtelxBWiEP2Mr70Jfma5exMFW3p/XXOP234SVi2QKkJ1uAiP7h5Z6SVZBW8rzeG+siHmvFsjTeMC0g3SjI+ve6SGtWtpQjgbpS0pql5xdYmLNHK7h3EYTT7o66vj/9SNWk82wkSVp1vUXMZSH3+WnRIielBUhdSUvHvHSON0uGWvW4irSiW9OsHu+Vk9Zsc+csBl5u/hUKnZ2DfCdQClhDkOulMgaRZyPNyFhjkXMVSOpK0QT3sG6Wctp4867DqF5P2XzzkNZCYwCF5VdaSQusKY+3L0enwttWaMpqTytYi7QaHozPqvMqWjRcGWlV8DCrivHm3V/a9JiHtBS/r1hc2FHAOsuNGg93P7Vp64Xl8G8hm3dGChW4X+uRVvELBpOR1cu+aNFwVaQ1q1+riZWcNt68+ytrvqXpMRdpqTVGtJCW7Jkev7IVZSaCtNZ/F1DH6b8NpKXaNayKtJriGi7vr9QWOIpdw60kLXGaw9NAwcKVMa3oxnGj/t/RqfE2+9TwryBpVetCVUJaDXENY/vraJV7qFWPOUlL5VjKI60Uoc58cntvfzwYnBSdKS1yAIH3qoo+kbSWXMOUFiB1Ja2s1ibGuoYJ453dyK0gLR3zbVZMKyNQKHtPCevHsg7CmJYvSKCqBYWB+AWXJLUFSKGFFaWxuIz8BDIMc4fU15Oqnpfu8WbdyOnSY8chP0LiaPicV7Iedd24F/4PsgY6a5i3lHAGLqLH+aUqAqWY8hC2AAkW+0vLcp7I1jplImr6thj4Zd0HdZ+XovH+umq8ojwmxXpZ/PfJrVx06XGe2zjvQmouaUmTMIEEoom8hOZ3u8Pxp0BW14e7f4SeVbrLK2ZJrDlO/21ILkXUA0AcraiZgNkEvPohD2NICzB7tCHFcoHJRA8zwvt/r2TaQxXKPxawZ737GWZ7Y8t4ELVy5Q9Vl8cUHmf4VuWh6nBKOWRQUsG0gacGvlmHMALCRVRcHlNK2EWxa1gaadXlJDDx1EAgchkGosc6e666g8KmCHMx9bxJUPpJ0JRFkrd/EQKhC1F30KsmWlsQItJVlF6uOwW9sCp8p64shJcL9Ad8+glh3mFKv4meqDOGuETMmnVv6Pp7pfvdTXARm/CqEKK5MO01njYfXdL5N0tn3DzPmZuM8MUTehutLATC0D1aOvPC45qu/0VtTzGvvVfnx2YRCCStDXDZ4zummK/rWorxx1URCMSWkBYCgUAgaSEQCASSFgKBQNJCIBAIhfg/xkVWDyfjbS8AAAAASUVORK5CYII=)
Let ![](data:image/png;base64,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)
1 = A(t – 1) + Bt …(1)
Substituting t =1 and t = 0 in equation (1), we get,
A = -1 and B = 1
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPMAAAA4CAYAAAAo2c5IAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAeTSURBVHja7V27cttGFF25tl3HspednVpcsbQrDb2K7ZJxSAwbO2Gh0WDixwwKJYHcqbA/wEkRS1WapMxMIn+ApR9QZiz/gK1fsBUslgsuQTyWJAguoFOcGYkkdi8u9uCee3exIC9evCAAAFQfcAIAgMwAAIDMAACAzEDKhSRkZYhL8IOdfli0bSBCTQbwdrd97y5r/EYI+9D3/Wvwg11+KMM2kKEGcDl92miQk2DAfLnIZLbZD2XYBjLUCD1G9i8ymavgh0XaBhJgEMMPIDOAQQw/gMwAyAwyg8zAxSCzmsIxwArIDDKDzBajy8ibgKif80C5+xRkBplBZvgBZAYwiOEHkBkAmUFmYZvnrVpFZr0QYeNFzSqS1Ani/AaDzlXOyF9ioGxs7bC6n3OmH9bJn7b5oQzbJjo0rCBe8v3+tcCa9zYunRPnsbO10WSUHIWFkhv87WBv73JdB/Fun92bKA4x581FI3OyH7pW+KEM28Y7dNh9Sc6oQ/H3eeyzAOxUkTeUDZYNHL/LHhBCP7Uc96Hv8rUGaZxw11+DFAdqrUz0f7bb9BllzksVxSQpyDlzdu9HRAnIIX4T/i2j8wf9+2VDRGRKyFnSlAUA5Cm6WpB5b29wmTP+ky5HZbJOz/SoJsjMu/4dLQKe2RL1xMXoNcmBrhwAwEjNBYGpSZqHVR43mScnoi6h/DAt3wzJrn2fVXCK5+Mpn69on03dRqAsngslQdvbz/Xj044rqn8AZLaazMP8+TxNriqyq+9FxJYFJ3rGuv4D/beeN7ji8NaTQP5+lDk3PdvY2mmGaoCSQ5WbC7kuPrvLGr/Gi1YGbeg5flgAEuTzBoPVHqOvonyfNo87Wzu3IjUyZ/8gQrJCmnUpJsi8ADLLKJcuoSXZ5fd+l99pcfdxFM1Zb3+Uw3ZuBUnscWOdv+66/s2QQDfIW/03Uq6zD13fvem6u185YimfVlQzaWOUFowq66LdgHyfVB0gIm+MqEX1D0jMsxQTZC6YzNFgzZDYIdkDUrjuxm3uPNlMKj55Xn9VkntEDBHhJBFGn8mKeG/fcZzNeD+mbYxuJPIzZUu80q7fhIrsH6i2evC8znVB5o7nXbdVPcxE5ryKsCI73dx8ybnzKC2a65FyPK8dFaiiijhz/KS7okkbo+g6ksoh2RIKYaJir9tYVP8Zg+ZSnbEgoi3czhT18MVkLthWv88ksaOoF0RuNaDj0TyKlM3egchbt7utbqNB/iOUvRNSNZ6btxz3u9QiXE4bcdKF02fiZtTefjZBTlntjqR4Uf1nDMzPdcYicuay7JxVZlvi+5VcMmdFtXGyky+sv3svLZorkoR3u0bjROab7pq62ONtJfdl2kZcYqvj4vPfSdK7iP4B5MxWyuyIlAlRbYzssXxxGM0/qWgeESpW2RYkcDh/HBWkhFxP6cukjbjE1vNivdoc5bmajUX1r0UiELyiqBWZ1UJwKUODAdze/iFJmysJq0c9vbrrttvfhlJXRstTUSTrbHlfi7ZEVXiT0j/UHVndONJWkJm0oUnseB5+KuzpDAZXw/OSC2A+6qlDEf2PlAw9Ez4rskBjU7EIZK4QmcW+vpNSaHzwh9EqXDDO3usnHU35BPmynksO557fqbbU1M54n+NtJd08stqIz3enHSemp8S0k/6bIvoX575Jyb/xNevzkkfcFE3z8oUOcnH+bff7uhNajiP2Ty3nmStzEeQcsRXLNx3G/HntCCV80I5ND4aIGzhlvVdII0DmwiWfvuxSyOdlF1KEHSKCiYUz87Ylag/LOJ+89yAJFSOWyYI09lyTypM5nCdu9g4GnlymqZ7gWhaEzHY4f6QWzsyTg8ocvnmcF90Lf6jd4D1IMqekxzYuYbVpA4Iyr0nlyew6rYdyfTT92OLOj1XbdEBU1dus/XOS3WHxMWdVWdbxM/vU8D1IcpmrXUtYF+EPG+xQ12Rlis0/IGdKvnOnyeikWYJpji8CeXtnyam6xexfVbQ/62LHNPuZgWQlIZwe4zd2h/PfE/s/xZeZTnt8GQMnuuHE5t1t9Gdd7ACZLcNun98ePjoZbcEUv4tnXTST40shc8JTcbb6sy52gMwWIpoPT1htFi08ydh4MOv4sgaOiZ02+LNOdoDMNpI5Y4ulKOJlkdlgi6Z5H3AwJrMFu7GqTRuXPR+fZ8eirwnIvATEt1hKykWz5GvW8QrOnA84mJN5+fu+mfjDBjuC739f5DUBmS2TYnlkLktSVoXMF0Vig8wVk9hjZE6R2WXtgloZMldEYoPMdZbYnnclKTfKy5nzji+fzMvNmcvyhw12TPNuKpCtPCn2XCy60Dd0mCBJAplNjp8Xpu+qsqGaXYY/bLAj+d1U5ysg8zLJ7HZvindyUbr+d9b6bVm8mox4psfPA9N3VcV3dFm+P91v6mrHLO+mAuEsQdKuofbdmPKXnALLA5xglxw/tWGpZKqNFj07DoDMVsPGp5J02PjGTwBktljGsiNbnkrSIV8GQI/walyQGTDEcEePZ7Zt0RO+7hevyQWZgWnlNn1pU5Ep3NSPOb/g2oDMwEwRmnds2Z2ziL3NAJAZAACQGQBAZgAAKoj/AZYMD86OG9z7AAAAAElFTkSuQmCC)
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![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAA8CAYAAACn3RK/AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAWkSURBVHja7Zu/b9tWEMeP7ppmdhw9bklm8VljOwXUM5x0E1CK0JIfHAiCqJ0AHIyG8uah6Rykg+NMrYduQdHY2ToE/gc8pP4HbP8JtlseKf4wRf1yRPHZOgNvkEyDz/c+vPveHQ82NzeBFq14kRFo3Swggp8F2j8BkTXof7R/AoKAICAICAKiJIPuBnE7jt3BjwKwu0BAzDEQbQ7bAOzkob2huYKtA2t+tLa2bhEQcxwyEASVN98Kw/++xL0pkPFGBITEQPiuqDMm/ijLMyAMjqGvNrn6GwA/6vj+HQJCdiBAO+h43lIZ+7LRA6lwGLiICwJCYiDwybWs1m0hzCeBlthpGI7hut3FsvaH9yAgJAEiG8PjON7t8FVg/DMeEOoIxs1fyhSUBIQkQKAXMEVjjQEcB9ecK8BOMauY9f4ICAmA8OzWA40pB+qyeGO4/r2tLeuWqME+8PYOATFnQHheZ4kDHAE336XfWd82QyDS78Zdu5mQM2IpBISEQLQ1eB8cwL94ALGGcHT2Mvjuy6BDGfGEb2PIGbWYsNcJCMmA8P3OndA7aD++9yxryTEaBqZ+KCIxdFSxPwKiQiC6Jn+En8OnVlUPIw3h1uOMg4CYUyC44T/OXbNgCvG0in7F3AOxm8v7KwgZX6DW3G/Z3gPcw4bdur/C2O9MuOszBjUqgHH4E4EIUl5e1FW98UCkIoydCtevz1pUYkmaM/jc28NxnHrO2rBhAQzg7JL45O3tKoDIF+iyD2s+lJayAd/gj2OlX0Ud4rrXUabtpVBcM8b+SQANRDZ60A37Iee6+6x0IMLU7wo5PwEx9LqFSWFwDN5mACdRluXWUy9q3AtDK+ots/uoVCDi1C9/IwLi6vtHm2qg7Y3rcREGO6y9KBeMG4W9miik9XvxmYaLombTGPFOISAmAyI6gyD9HuKlwwdXbb7Nw1KYHVylRDssXODfYKGozdnrWGApTDto2Rv3s9dhvDMEX48bUigKue48H3ZvAqLYQ+MrgsNEfXgdN18NzDLGL9EOTt8GhYufjfoPDJSTuNUcNpsY7EFN7MeEYr9Br8EnhECYaytxxhDAcYqub9C9CYjJvcPM0s6icBEoWS081NwGoyJSmpo6OnuRFzlJlzIDzjwAkffWnte6GwCx3/K8u8Hnb9Lf9dc1okJYv1isBIgoXKQt5uRACzRFBEAKhMnhXb52kcDExN4oIGD8kFf5GgVEz1uf5bzzRZ/HztU1UntfvQY0NQ0Rh4usW49dPtOdF4XwZEDpFXLOY82A7zT0/rlj3umujnrCxgl3sqyyQsZUgfhaDRGFi2gjMTRJbyHnvgaFEVfnz8K8uXcvVV3+MKrKSBri8oo8bX8/pyibKzVkhE984NrdrruIL7BmdUL21bXkZRUUjzmKsaIWKF9/kiYUAVFYMr+Amv6pZVm3i0BAzy063e9KAyIJF7rz0jeMerzxpNnEjR3cHKaVkejph6EXXk6Y1v7VsrylcRtkBET/whGAqESNqX3Y5AuFKKb+JuevGsJ9WqqoTEqhrPkx7+LzzSZMPfOvvSO12JVcVtUPl8ITW/6rZdt8WO1jFkCUOQs6LhAc+N+T9IbWTLHSs+fZRCFYgidEcXT+PEtt13UXTSGeIEg46DIshZoFEGXOgtILMvmYF+oMflQ0QYV6A1Vz1UCEgrekWVAColgEnTPefo06IynGYLwTzEc3N8xVzsqgZc2CEhDD412a4qrqYUOYP406gJkCUcIsKAFRgUr/Wo1T5iwoASExEFXMghIQkgJR1SwoASGhQaucBSUgJDPotGdBCYhrDsS0Z0EJiGsMhAyzoASERAaVYRaUgJAQiCpnQQkI+UJGpbOgBIRkBq16FpSAuOEGJSDIoAQEGZSAIIMSEGRQAoIMSkDcACDOr/n+zwgIWvICSkagRUDQGrj+B9SG8ecbP/FOAAAAAElFTkSuQmCC)
Question 22.Choose the correct answer
![](data:image/png;base64,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)
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAA4CAYAAAACaT/nAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAcUSURBVHja7V0xc9s2FIY9J5kbx9CWdjYhje2Uo+E6GdWY4mmpUw06He8a+06D70J58/WS7kkXx1Oud+3YtHW6dbH/QJf4D9j+C3YqEKTMUAQFWiQIUG/4zjnajvXh4QPeeyDeQ/v7+wgAAOgDGAQAAEQJAABAlAAAiBIACCcYQksMNeKynIIlECXAGPgOeULc0WPTeRwc9O5sYPT3WIDXY3wKv14xYNx83+4PvwJRArTHcNhdsRA+pZ6/VhdOnk2eMUFGC43vOQ8pRscI4ctH/T0LRAnQ2tXrEPSWTdY6iXJg4x2EyMeu79+Pno1c8jjYPUnnLYgyRywTiwdqEd+YMHkxxv+OJ/BZfAKb7sLSVfQBEfcw6aIzUWJ7sAOiFIix328TgvGfyOocRc+Y24EROkeYHvcODu6AcMrDXv+RhfHGO5div06i9D26Np5Dl/EYmc0th3sEF0V5BLWbEKMu2QwD8OvIz3cJeeF4/kMQjIo4sneXNpqvmRAD93WVfqjLIhi6rmft4fAB87r2+u0v10njzXienbdcb6uwjaWuk8NzW0/ZqoawVatEgwmJENIdbbJ/10mUE9c1lnVlu+Mq7Yzavd69Qr29uk6OYBBZVqxGK7URbqvV+ZntIr1e+x6Pv4pJfujmurL5FS78F2jV/qc3HN4FUeZwN+oS02jvtgZHA9EuEqCw5Ieuc8kl6LBonjWeJN0V2mz+FKxujv8EhFMe+PEHfhUPE3y/e58gdFYHUU5c15QkIRcriDJzckRwKd32Rt4XcRcKjkPKGXN2JNCi3naWu2e8Wz7mEhce4828g/UwziySZ/3cVatz5Ln022jVDtyLcVzZ77ctQtwXIKRiBTlwWg7G9Nd4siN4bpMf2A5C7AH7umwqPxYbb1noKMzkk+h914Fjb46Vehq8Zkfcl4X+3TpNEo/i52F6+mn0jB2RsPNJNnCQ8CkWDo+nePwYunaxd0Svkt8zjV/seC0F+Bzj5h+O560VvhjA5AIANNuhYRAAprvQIEoAQBOwDK+FrOO6HXmBcQEgShAloExXTnAzvtSb8iBKECVAADeeDc0Apt5zECWIEgAo3BMYDtsPmCijWxt18QSSpJcBZqCkSa81RyfdE7ieekacQ925ZXFNfvArgBkoI6Y0geNt3VeT7AluEcSUEFNCTAkAgCjnEqXuQXPez2dSEgButYAoUyeFZ9vf6Vrfhl0PIrb3THby6s5nHm6LKkqCyF8LI8rgTiIhvu71bYJbIKTzatbkNYXPbbgB6gXhNwY23tUhIRC7uCw8BmBXtrA92M36f3ThE+Mkda4mw834SShh4xrwkz5HTX3Ib1pbp1W7BfwSrb25Thq/ZNXa4bEFPhWVjdeFzw2nlhNU2gt6UuBLVmxKVHhpFrc6TFgZG5vNb9reWRXwUh922E3rRBXoKsB2iUYD/ccPiLMNFhwHCCqn6cInEBmvpn2dOPz+hFapsCJaFjfTkcfGRsa93N5X0/YWV8AT7Cp61VbhPSmyDcb7OUz/jE58+K18/C5eGeFHl24EZQpZ6QzBZxRxqxNkbGwaMux9nmXvtNhrR7Ypi6p+HTIGmxRqSlSuk+Wjggv7jNTxv0kXndhIIm6qYr2y7VuFKJXZuzv6WmDva2lRygyO6n4dUqIMSxom3bxZv6tD75G0Tk4y3MqcsGxMmhi//2xMaGu7rDFRJcokt0icZXLLa++p7TYoyTijqrjqfh0yBkv77DJ8dOg9wvhlZYZl7VIUqhgTVaI0wd7pK7Kk8WX7dcz7onQuUcZ+Lg+fPL1HirxMzGNecpKXm5IkjCL7VuG+TloOaGjv1NhF1k2S7dcx74vS+UR5Ez/m4ZOn90hRL36zYr4sETBrUqRxU5WokBkTp4DxUC3KPPZ2FNt7LlHG/ONSB1OFKFVxia++8Q5VOopS5ZhUkX2dcBsOV3Syd7ooJd1XVf065halBB+VvUd4BXG8k1xZRe5PVaJUOSaqRRnjdqGbvXPHlFX06ygrpqyCS1TSPyrnH4GVx19vkDdpHFXGlFX1Y1EhygS37+PckkckVdo7d5ZPZb+OqJcDJeh3ZrCwl8NSUdlX1b1HwhVzl79ulQLBW0cqs69VjElg4yb6bZaNTeSWbe/0sEqQxBCvWCr7daT2chBM3JuzvM+/n8VHde8R/vfEiQJRvCHiVkpWUvGYpNvYOSyZ25YW9pZ9eYC/baA+oTAvRK3XTOUjww1QTwhXZdMarfIXf6d3RFP5pHD7CB2pF1SUE5fPsFsJQaJA4N6ZfssiixtgQUTJ3SVyouL8pgiw9DZB+ETkoprGJw83wIKIMgpSWTtpE0pRpJ0BmcwnLzfAgoiSu334pe7JhaDAlGQq2wQ+t+UGWBBR8h2GtnWuZtei3nae39GZz7zcAAsiSgAAAKIEAECUAABAH/wPrejxKbEQTQgAAAAASUVORK5CYII=)
x = A(x – 2) + B(x - 1) …(1)
Substituting x =1 and 2 in (1), we get,
A = -1 and B = 2
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= -log|x – 1| + 2log| x – 2| + C
![](data:image/png;base64,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)
Question 23.Integrate the rational functions.
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A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM0AAAAxCAYAAAB57C0LAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAeuSURBVHja7Vw7cxNXFD6yWwxtAN/tCCnxXqlMR5brYJhJocBqRw2GHY9GszPYMFswRqLzBJI6IQXginGRDibhUaVh+AFMEuwfAPZPQCh79u7qsZb2rUXynOIbQKzu47v3O/ecc88K7t27BwQCIT6IBAKBREMgkGgIBBLNkSAOoLQDMAdQnSc+SDSECHQdwTSuaCvfceV3AL5Xb7VOEi8kGkIIGoKtKwq8KwF8JtGQaAgJUOPwhERDoiGQaAgkGhINgURDoiGQaEg0BBINiWamIe+fYJ7uoEg0JJoYsG1zYZnBC0c0n0qg7lZt+zStNYmGRBOCpqisio32Ofy7weExLIpX5tbWMVrvENF4R/NcYQOAnblZaDOraIrmdaDPUtrvtyyxxEB9W6RRwPECdEszIxq7UT2LpSFFEdVq1U9y5cLDPC3ZJNoctbCmWT2hcfgDQN0737jDw4RaNK8IZ3zHDc4e8Hr7YiYugb+Y1JhH1e+1N8Q5zo1W1TSPFyoEV6x+LOdibpyIhwhSAf4rsjRkVkXTrvOL6PMPgdcejRtP0byiSMuMPa8Y1pUs7dxpnFcrwlqdxBjD6vewTImx8vNqwz5bhFjQADb1is4Y+7u3noy/wf4dDjjXrOuh7lmRfvq0iKYIt6koXlt29bQKpd0sJ4y/qQ0hVpOuTVwuo+r30DDJRETr9KTWEefY1HmNQWkfRaJb1lLfNdXPOO7De+eRLjfaKySaQyeB+nLS8y2CV7SaNRW2gRuPswqmqbENX3hx46I0XIbx4iYi1Np2nP6T9o1tNjR2y/njM+P6g1H7RXoUfDfYZuxJBP29URPx/ELvmehgPO4G7/ub/Ta7vb6G+5lF0eTFLbpTDNi/wmotpeURY4w1jd1m2tpt/Nx2Ti5Ns378EqLBRIQCyj8YM+bd96a+dNmZXzfMwGCbZUX8FtxLkZNAon0fue/vqW9l8Ntf3C3bXNAFX2cAH/EZhWsPnWDuRNgix9ngrkVoVDln7E/f6uBCW6KyqgB8AHbhxeD3Z0k0eXPr9jEmRRyXR6eNR8PxmvJhnAgnLZqtLfOYWIRXTrz4JM++bbt+yokz9wDYftjc3L3Ejc3Q7NmoSWAghD4fE431nq/H4A2qdEnfvOx/r+kedc4gNtrncLLu0YpKBugEN3aSDT4QdHec9g9wQxmc39Wt1plZd88Sc+ss8Dhu+xtstOVMymNa1zhP0fRctEXx2rTthbz6bun8UtQpE+r5hE3CW4jXQesl8/ew7z8nU5OOcgcsgvfMQTCISrvBLaNyxe3TscSR1iGkzZ1hV2jesqqLDtmvqpa1OPh53nc9wc3R2+RZuNVbl4bTw7DHtOZGHjzGQR5cRokGYysUeXCsWfqWfUI3bG+mFo2/OMHjsbfg3mTcfzN4CYtazyJI/xoOwhYxiWj6fYTfUEe1edj9cPE5bgo5L9Hkza3fXpRo4vIYc06ZuUwrmrR9B/nNXTRtg6/IY+ywTxlUKx7/aMG43qyhwmVmAjphqc+krpQkUN2r2/aporNnw9YrGlGbI29uB0RzKw8ep8U9GyeatH33jIZ0UdVJnTT7g1Zu+Ll+IIVBZY2znzH37geQUZdrSTY4Bm+iXP5Jbp6+W1KgaD4lQcyTJjduR7lxWXg8qqLpxUmBuHFMprGUQDTSCvVVOdwBZnM0jHXYci/Ax2DVT1PG9WejNrhMh+64KVhDiGtW2/rKz6aMq1Ga7kRA37qHcXsB55iQ2157I0SThsdpEY33/7tRbSZKBLgXp9BBgzWqXAf5QhdY1NvfhoqmV0+FYvAWEsn0si4dXPAfzI1vcLG8bM5Hvxp2cAMcgmtJtxbSiMa1Mmpt2zLE98OVt9rrRqOqcm7cnXbRjON1OKM1glvPsibh1hJs3Y1VAidXGh4nLZpD9XumXQ4a2KiMYJZ1bAp2U2Yf1bc+9+69lGmewqxiRTRXI90zLJRz8/UDLoafCnWL6GQq1P1cUcrPgqlKS+PX/XuEADrjgtOoDY6lFkFXBDcajpPx2v20aezDbg3/a1KiCeM1b25lX+5loJqVx7SiictlnPo9tPY4nzgBe5p1vGmI5bKiPBscwyj+I92ztNa0ofEboyaHKc5xRX+zWrBZJJJyi1mlOfXqNmR4JWB65u2cujlnMXMZWy7WFDNBYy6g7jSqX+u6dAlINJPn1ksIvK/oTb2o94omIRh5AcnfT+MLfrk0Io9/9pFrjRv98g6Yx0UVwrhW5AYv6n2aSV6EZuVW1kwpz5gwWlE36dMoGOcEvRrHTZpp0fiuQj8l6kBR3sVJOZcV7de8RZN3m8FFleXkcCADcnbA1Ku/VE17Yi9NpeEWg+gaZ/ezviJQ+MkqX0LbnGZPYebdl6Lh1S11BoPxfiZrtqw6gUQzcaD1Xmbs6aCVxwyMl9lKXctEINEcWaDrMOrCS5bElLqz5goRSDRfDLLUI/rWmkCiIXiJASz1YMJaJz5INIQYkGX6/A2dMiQaQgzIn3BlT/16LgKJhhAC9/16jV+n4J9EQ4gpGAz+BwsvETsF/+wsgUQzM4JZ07jJtTVzsJTGLXNX+EOKbUg0hEOCYbdHvtuS4ddNCCSaIwtZPDn+FWeKb0g0BAKBREMgkGgIhMLxP/71QJkOC299AAAAAElFTkSuQmCC)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
1 = A(X2 + 1) + (Bx + C)
Equating the coefficients of x2, x and constant term, we get,
A + B = 0
C = 0
A = 1
On solving these equations, we get,
A = 1, B = -1 and C = 0
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Integrate the rational functions.
Answer:
Let
⇒ x = A(x + 2) + B(x +1)
On comparing the coefficients of x and constant term, we get,
A + B = 1
2A + B = 0
On solving above two equations, we get,
A = -1 and B = 2
Thus,
= -log|X + 1| + 2log|x + 2| + C
= log (x+2)2 – log |x + 1| + C
Question 2.
Integrate the rational functions.
Answer:
Let
⇒ 1= A(x - 3) + B(x + 3)
On comparing the coefficients of x and constant term, we get,
A + B = 0
-3A + 3B = 1
On solving above two equations, we get,
A = and B =
Thus,
Question 3.
Integrate the rational functions.
Answer:
Let
⇒ 3x -1 = A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) …(1)
Substituting x = 1, 2 and 3 respectively in equation (1), we get,
A = 1, B = -5 and C = 4
Thus,
= log|x -1| -5log|x-2| + 4log|x-3| + C
Question 4.
Integrate the rational functions.
Answer:
Let
⇒ x = A(x-2)(x-3) + B(x-1)(x-3) + C(x-1)(x-2) …(1)
Substituting x = 1, 2 and 3 respectively in equation (1), we get,
A = , B = -2 and C =
Thus,
Question 5.
Integrate the rational functions.
Answer:
Let
⇒ 2x = A(x + 2)+ B(x + 1) …(1)
Substituting x = -1 and -2 respectively in equation (1), we get,
A = -2, B = 4
Thus,
= 4log|x + 2| -2log|x + 1| + C
Question 6.
Integrate the rational functions.
Answer:
On dividing 1 – x2 by x(1 - 2x), we get,
…(1)
Now, let
(2 – x) = A(1 – 2x) + Bx …(2)
Now, substituting x = 0 and in equation (2), we get,
A = 2 and B = 3
Thus,
Now, putting this value in equation (2), we get,
Question 7.
Integrate the rational functions.
Answer:
Let
x = (Ax + B)(x -1) + C (x2 + 1)
⇒ x = Ax2 – Ax + Bx – B + Cx2 + C
Equating the coefficients of x2, x and constant term, we get,
A + C = 0
-A + B = 0
-B + c = 0
On solving these equation, we get,
A = , B =
and C =
Thus,
Now, let us consider, ,
Let (x2 + 1) = t
2xdx = dt
Thus,
Therefore,
Question 8.
Integrate the rational functions.
Answer:
Let
⇒ x = A(x - 1)(x + 2) + B(x + 2) + C( x – 1)2 …(1)
Substituting x = -1 in equation (1), we get,
B =
Equating the coefficients of x2 and constant term, we get,
A + C = 0
-2A + 2B + C = 0
A = and c =
Thus,
Question 9.
Integrate the rational functions.
Answer:
Let
⇒3x + 5 = A(x - 1)(x + 1) + B(x + 1) + C( x – 1)2
⇒3x + 5 = A(x2 - 1) + B(x + 1) + C( x2 + 1 – 2x) …(1)
Substituting x = 1 in equation (1), we get,
B = 4
Equating the coefficients of x2 and x, we get,
A + C = 0
b – 2C = 3
A = and c =
Thus,
Question 10.
Integrate the rational functions.
Answer:
Let
⇒2x – 3 = A(x - 1)(2x + 3) + B(x + 1)(2x + 3) + C(x+1)( x – 1)
⇒ 2x – 3 = A(2x2 + x – 3) + B(2x2 + 5x + 3) + C(x2 - 1)
⇒2x - 3 = (2A + 2B + C)x2 + (A + 5B)x + (-3A + 3B – C)
Equating the coefficients of x2 and x, we get,
B =, A =
and C =
Thus,
Question 11.
Integrate the rational functions.
Answer:
Let
⇒ 5x = A(x + 2)(x - 2) + B(x + 1)(x - 2) + C(x+1)( x + 2) …(1)
Substituting x = -1, -2 and 2 respectively in equation (1), we get,
A =, B =
, and C =
Thus,
Question 12.
Integrate the rational functions.
Answer:
Dividing (x3 + x + 1) by x2 -1, we get,
Let
Now, 2x + 1 = A(x – 1) + B(x + 1) …(1)
Substituting x = 1 and -1 in equation (1), we get,
A = and B =
Thus,
Question 13.
Integrate the rational functions.
Answer:
Let
⇒ 2 = A(1 – x2) + (Bx + C)(1 – x)
⇒ 2 = A + Ax2 + Bx – Bx2 + C – Cx
On comparing the coefficients of x2, x and constant term, we get,
A – B = 0
B – C = 0
A + C = 0
On solving these equations, we get,
A = 1, B =1 and C = 1
Thus,
Question 14.
Integrate the rational functions.
Answer:
Let
⇒ 3x -1 = A(x + 2) + B
Equating the coefficients of x and constant term, we get,
A = 3
2A + B = -1
B = -7
Thus,
Question 15.
Integrate the rational functions.
Answer:
Let
1 = A(x-1)(x2+1) + B(x+1)(x2+1) + (Cx + D)(x2 - 1)
1 = A(x3 + x – x2 -1) + B(x3 + x + x2 + 1) + Cx3 + Dx2 - Cx - D
1 = (A + B + C)x3 + (-A + B + D)x2 + (A + B - C)x + (-A + B - D)
Equating the coefficients of x3, x2, x and constant term, we get,
(A + B + C) = 0
(-A + B + C) = 0
(A + B - C) = 0
(-A + B - D) = 0
On solving these equations, we get,
A =
Therefore,
Question 16.
Integrate the rational functions. [Hint: multiply numerator and denominator by xn-1 and put xn=t]
Answer:
Multiplying numerator and denominator by xn-1, we get,
Let xn = t
xn-1dx = dt
Therefore,
Let
1 = A(1+t) + Bt ...(1)
Substituting t = 0, -1 in equation (1), we get,
A =1 and B = -1
Thus,
Question 17.
Integrate the rational functions.
Answer:
Let sinx = t
cosx dx = dt
Therefore,
Let
1 = A(2 – t) + B (1 – t) …(1)
Substituting t = 2 and then t = 1 in equation (1), we get,
Therefore,
Question 18.
Integrate the rational functions.
Answer:
Now,
Let
4x2 + 10 = (Ax + B)(x2 + 4) + (Cx + D)(x2 + 3)
⇒ 4x2 + 10 = Ax3 + 4Ax + Bx2 + 4B + Cx3 + 3Cx + Dx2 + 3D
⇒ 4x2 + 10 = (A+C)x3 + (B + D)x2 + (4A + 3C)x + (4B + 3D)
Equating the coefficients of x3, x2, x and constant term, we get,
A + C = 0
B + D = 0
4A + 3C = 0
4B + 3 B = 0
On solving these equations, we get,
A = 0, B = -2, C = 0 and D = 6
Therefore,
Question 19.
Integrate the rational functions.
Answer:
Now,
Now, let x2 = t
2xdx = dt
Thus, …(1)
Let
1 = A(t + 3) + B(t + 1)……………….(2)
Substituting t = -3 and -1 in (2), we get
A = and B =
Question 20.
Integrate the rational functions.
Answer:
Now,
Multiplying numerator and denominator by x3, we get,
Now, let x4 = t
4x3dx = dt
Thus,
Let
1 = A(t – 1) + Bt …(1)
Substituting t = 0 and 1 in (1), we get
A = -1 and B = 1
Question 21.
Integrate the rational functions. [Hint: Put ex = t]
Answer:
Now,
Let ex = t
ex dx = dt
Let
1 = A(t – 1) + Bt …(1)
Substituting t =1 and t = 0 in equation (1), we get,
A = -1 and B = 1
Question 22.
Choose the correct answer
A.
B.
C.
D.
Answer:
Let
x = A(x – 2) + B(x - 1) …(1)
Substituting x =1 and 2 in (1), we get,
A = -1 and B = 2
= -log|x – 1| + 2log| x – 2| + C
Question 23.
Integrate the rational functions.
A.
B.
C.
D.
Answer:
Let
1 = A(X2 + 1) + (Bx + C)
Equating the coefficients of x2, x and constant term, we get,
A + B = 0
C = 0
A = 1
On solving these equations, we get,
A = 1, B = -1 and C = 0
Exercise 7.6
Question 1.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = xsinx
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 2.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAVCAYAAADxaDaPAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIdSURBVFjD7ZexbsIwEIbvAfoAIMXdeAC4MnarUgt1rhosJhBTdRJirgwbUsULdOtTdOnahTfowBvwDjSX4NihDgpQliZDBiz77v/su/8EzOdzqOpXWfAa/tIJ+iiWALiOSLdq+DM+TbLdEbACgC2A2GBIo0qUPYN3pZqMF4urxWJ8paTQfAmoZg//Gp5hB+HgcX9NBvAJ2H+vnOEZeBE+T/8Mnihq3wjx4d4ohTgSABsI5CeXXVaKetA0PXiN9298FlFpW6pR6x6v3wR0VgOtm0a0kt0Jr0WaWqknxD0sOitJun1MGwjsL8/Rnzs4U/iQmklqKCxGIeois+ojvBvTYSj+bZLyxSDAOo2FawOf7NnFNz2cgLC4EiXMeUh1nwSIb6mod45+b4I0eCzmwGsYONdwkjXn5S2shfetZf279zJFOS0gbH1lX0Z/IXwZMdmeXckfqo6/gs9emKiRtcte7GPiFSZ4DsXUFzjfd1HLzl1/314CPh8nLe9T9BeWl0R85dIpM0eNsfle4pLwaY//hi+r37uopBzSjBqH5igLDjF8ccUaw3ETXhzec6aM/hx8UibxRlKyZ24yERkH3x9huTkbjxuTnI3GC+VciF2zL2aNzF+mZhq43sI6gyD4MjGO1f8bnsePoif3ZjmpC5iDl2pIdHeb9b3T89n4cp1ZKm0uw44j1cs7+AEDc86xJqJZ41T99V/aGr6Gr973Az9YfE31zwGDAAAAAElFTkSuQmCC)
Answer:Let I = sin3x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 3.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = x2ex
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Again integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
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Question 4.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = xlogx
Now, integrating by parts, we get,
Taking, Logarithmic function as first function and algebraic function as second function,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 5.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEEAAAAZCAYAAABuKkPfAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJJSURBVFjD7Vg9bsIwFH4H6AGK1MfGAeDB2hGsqgdosDqBmJCligMYNqSKC7Ax9gRdegJu0KE34A5tHfclwXISB1GqQgYv0XPs7+f9JLBYLODS18UTUJNwLBK0iloDaq4ROttHrRsXR4LWjw0C+ACATwD6OBUJSvYeEGBnz8Ud0nA1WS6v/jQdhgSbU5Ewl3RvwTvrRrwdSsS/ImG5nFwJxJeeVA+pK8Qdu4Lk/P7sSdBKtEWkb/PccTQSlIraXcRXoOEmedanccx2juV8JJiCGb+H7YqdrVC67SorRe+JlWzSYH2Ipad9nPlECMVSkG+4M5eWRDpSulXFCUYxcxD2pzMmpIOwddWyl7fnGELse6rnuNnHZx2Cpbj6etQrIyHO2xt4c0EwMRyXdJaMShxTxdZ2T357DsGSX4A8QEJISMBmwO29M6O8e4broNBCWSRUCJbKeVZGQmJDh4Q0Lk0JE2tAc7W3Z4YXOJPfIbFlWHKHIEH0HGpNrxM8zNs464T0Ga4Q4Z1zN9v+yoCFOCYEi3ejFGKk5uo6tpFH0aCa4Cjqs2UoEK8D+mrs2n7QpLWrdgiWfct8B5nhg5WKwX1f2rQaIqkLc86xOY/SXI2zncDdV2X645Txrh+QVbGA266yduSczZvN04qfXiRti6LNbTF+jt1Xtz0lPdsDyOeQQgIyIlTF8qdfb4YEX2U3bc21+1n+T4hTJsf2ZriKovL55N+TwJY1iu8PVVFLCDm6mD9L8TSXtEfzfYHvoS2y/r1Wk1CTUJPwW+sLmYg04eRg7asAAAAASUVORK5CYII=)
Answer:Let I = xlog2x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 6.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = x2logx
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 7.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = xsin-1x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 8.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = xtan-1x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 9.Integrate the functions.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAAAZCAYAAABjNDOYAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAJUSURBVFjD7Vi9TkIxFK477ppYNtzhyOhGLg1xJREaJwwDMV0cGIwpbCSGF3DzKVx4Ap9AB54An8FrfyiUUnoBr0ZjSc5wb3t7+33nO9/pBQ2HQxTDH5GESE4kB4nfQSTHEzcJvhXkpDi5uY3keGJA4SKSE8nxe4odkRwRo1G3QE7QRBDysRInZNIdjQpRObGs/ig525whNnnBtuNfOavMW7kuN2g/5XFGWpvU6zUrZxg/2y9gCVxjhGZujZvgrFWqYPRiNleE+qM9T46rNc3mceWl1rurrKzBr47NGvJ5xlplAMrzVtcu+NZkOQeQIoTfCeNlCsBbjJeCUkb4jVDW0ESQsnjRu3mRuTZyt4hMgQ4uzDptQE+QsGtjwPJ6HwVkld0u+LyLMFq9VABFhuUCWV3ErnMNDI8lOS3OSqrLOBlZEIhgesX5sVQNIDS1yVL3vkE5u+ALt84NZeSCtEH5xl0FLFuzzp7VqlNZUs3e3emPHA0y8GUYnM5shkzTTeSYcV95qLKxnnV8K83Kaj7fYmF8fkUISROAh5AqQspYG/dkSJOjleOaex2Kj9oXwpvfN7bF571JCemwATtS0guYovEK9TVMKO/2+4emXcsOUKXs0pSLvQlX1vI6geTePe2GVPmV2BbfqszEREZJw2RTZVcACLXVRem4MQe+7BAwlV4iidOSXqpmYezQHstnFLnCNPNUzj74nBrEM5nt1TaNZmbTm92fNIpF9Gqfc+z2KMvLPgdhfPZsjytyCO0wVjtfzMvZc/bBF/8O/S/fVpGcSM7viE8LfxVBaPxciwAAAABJRU5ErkJggg==)
Answer:Let I = xcos-1x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
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…(1)
Now, ![](data:image/png;base64,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)
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![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, substituting in (1), we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 10.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = (sin-1x)2
Now, integrating by parts, we get,
![](data:image/png;base64,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)
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)
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AalrBY1nV33/2Ah3TRYg8CRCFAFGoJSFfTIDoabZ+xesb3BFFK+JEJt6AnLXVLi15zRmUvjDl7gCkEiEKAKKQrSMOwblxS0Wz5iS+Ju8TgwmuxLSefIA3jLd24hAQjCBCFAFGoDbvRE+z4IEAUAkQhqDxIAVEIEIU0h+hodK5oEToE1QRS+CGko2/OzZd0dScguoQQZYbxOr4I3TzSoR8lBEGQThryM/PImXzYuGN4GxCFIAiCIBk7VhgBgiAIggBRCIIgCKpV/wcjp2L3+mrK/AAAAABJRU5ErkJggg==)
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![](data:image/png;base64,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)
Question 11.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANQAAAA4CAYAAACFWNbhAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAa/SURBVHja7Z0xb9tGFMfPe7I3QU5bsltHj+0U0ISRji4iE5pieBAMFmgKaDAK2pvRNh8gnpqtHTpncL6A9QlSIP4E9mewyiN59Ik6no4URR6p//CA2KEo8vx+99773+ORXFxcEBgMVo9hEGAwAAWDASgYDEB17oYI2enqdQuDYwKo1i3wvYN9NrgihN2Ow/BZt6597y0l5D6CaU4Ivafs6MPJdPoUDgqgWrFTl74fDMjXxCG7BdS5z95E1/2Qszl54X05ubx8AicFUK3ZESOfugTU5eXJE4/Sf/b84K0caaNodcehYv75GzgpgAJQhhYG3q43Cn8oiFqFQKnqLNRfAGrrgdKlsEX3MZkcDh1KPxN29CmLai47jqMa9a6RJgIoAKW4D+qevtfUW7F48XpyNvQZC0dB+BLODKB6C5QsgReZLg2khN3o7iFTBelw5gXhLhwZQFkDVN21h8/IXwrVbslUEUiIFKsgiY97Qb5ACQRQVgHFo8GQkhn/jA1pE6+FTJU9XZ3VdytKiQFUy0Alx/OIQe/aTp04IKZOEobjZx5jf/C0b9uk9cCjvxRFeADVIlDcKdlg/8qGlCmOTG5wLNdY0+nJ0/0Bu1Ldi+9574Lz4Ls47ZPUvm2xMpMPgKpo3AE9h/zLgeLqV1eASlI3rtopTIIlPi76mS/8imgaTyBRHRUEo13G/BBAbQCQkjW20clsXzRUtu+smLkTNW04a7MGSWEqFC7kdC45lt7JXRX8vvn6U9z71yNxYpUy2hRQC8sUhpmAQX2RzZjW5q1VLAGK/gfZ2S5LlE5yrZxkUqduMkIlfmJeq64kNF7v6KE8C6CQ8plHKXOhq1Y6ARSsSaCaKENEnWoaUAxy/H6udfR5smiyxlmn/q5SmwvZ3LQEKdtILP9fLFwRciu+x+Rc+lzWUJZdp9UGQHVtIhq9ZJTcCKcesP2r/MOQZ5PDV3EDr6h96HCWV165syaL6sk5NqFUahuJFVGHK6ji3vg1nY72Rrxnkmcxpuda2+Ek8aJ0qw2A6pYlNXWUJvvBgTyGskOJ34m/twTgnI3CH2W/4WtvYvKOW7ZqXFMr00jMv/+I0Q/xAn96b1m/JF+WiP5tei4r0r02IhyAqqC+RRmLPDEmINA/+WMj3E+Kegwz8FJ/EqkUB2whvdrAWppJI3ESFBa7ZfLpnum51k73ain6KkQ4Ewh1QK4Cquz5u251TEAZODm/yfwpTZ8kaXzOU6vDydmrTZUFqxqJix7mVIlW2XVrRArtwJimaW1EGBMIZSur8pU9f9fNMIXSPpYvjlFNxOnEmX0+V4vNVXVWnaqgKtvSwVak7mXnmk6fGwOVhsB7E0m52zVUvbJ5HyOTKvoUfU5VU63yKQ6W5ww+Jn5Sf4kRNxI7zu+q6FoUdbP119zEsHAuqR7UAiVyx74/axOrTITOagZq3jUzlZtTv/jGP0M9P+TKnoBSPHbymNotChD5SMB/dpn7m+xfJhGwiukaiVXfySFzHOejAE0eB5Om5KVBFM2aTS2c9RSoTqd6qao1z2cVi8qZZNLk+3gMuxW1kehDFGOdCRzp/oMxlPF3sm91RCjTRuI0Qt1F9/lrcg3eAVceRVrnuu7PjkP/zp8rViSjc3EpPS+kqAZLsnpu0Dbjg8f/qEWPR6wJ1EPXx0fIxKo0nTtWugditg6Vl4+5o8prVZQ6n+VjYqA8/10QvP4+O46ym7omt2Tx16yROFYpxfcLyTz9PN+RqmxT8vYtTArJdjw+zqcddQBl4+SBLcYaHO8+RR0Tx3mUbOt9Sjf9bquAkmqaB50yBQNQSylK23uDryryWxkXlx3nawhs6gKgtJatfbS8N7jt9ZMND1QCKMtNszf4fdN7g9tYP+VrxyEZXgMoAKWddavsDb6h+m2u+r1NYyWaUWEAqpQ1/RxXvn6y8V1VfFES9ROAqmRNb4Qo1082vquKXxO66gFUZ4pvVbpnyz7r8uPi0+n4uesGP8HxAVQpkaLpfSLaBEr3WPbyPuvt75ALoDpkZfYG37Qg0QRQeFcUgNp4atNkJMjXT00ChXdFAajNRqYSe4OXjD47uraiot+bAFXH80p4VxSAqj0ymewNXhGoB6kLY15Qr1QCap33SC3VjXhXFICqESajvcHXgUqGy6R+alKUeByH7XxXFIDq8mDlopSuIbYpoLb5XVEAqvtALUQpXUNsU0Bt+7uiAFQ/oNrR1U9l31VVKcXDu6IAVN9SPxVQVd5VVa1m2o53RQGoLUr9bH9kAwaguhalOr8hCwxAWROlMA4wAAWDASgYDEDBYFtn/wO8SEAH9YuymgAAAABJRU5ErkJggg==)
Now, integrating by parts, we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 12.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = xsec2x
Now, integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= xtanx + log|cosx| + C
Question 13.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
So, now integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAAxCAYAAABj0M2FAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAU0SURBVHja7Zy7bttIFIZn+6TfGBl1fgBz6DKpDJrwZssEoQlV67gQjFnEMaAi2NDujFweIK6SbputA6zzAvET7ALJE8jPEIWH1EgjRpZmaJLi5S9+wFA0Q+bM+eacMxexs7MzBkFdFowAAQIYAQIEMAIECGAESHMIxn4hAQKokzoKvN92Re+CMfGtH0X3AAHUKUmfH/d67L84CowBAdRp7Qv2ERBAgAAQQIAAEECAABBANRukCpctAUFLHKZN/59I+lsOZ1fkmIGMNgEBIDAaRO4dvWhXesK+M8ZHvoy2AAEgWKojj78gh2kLBFHUvyd6uxeH5+d3UBMAAisQAEG3IVA1lGlqDAhqXg9w5lxV5ZDD4eFd32X/EAQ7g5dOE+ur01A8StNHNmZi/2MrIdApz6qdEPD/q6gFNOeZSYQfmms3di3C00drgSAUIipr5jo/P7zjc3b502BpAwYIoBRo85Su0Ie/HOw4VYbvbqRDgCBXXXPf/2xaSxWbT95nnxMCh8ONbD55U/qS/U6ewiYDwUkMwYlNarXqs9u2qSqst0W2Ntb9JVlMYOybmghN+jLKtVc5pZamjCeaW9cmQPYFf6enL1zsv1Ok0r8HvjimKBJEcjMU/G3yPe5c2cyCaonUZJl0MHjsuJx/0osn6YmD2OlGjPuXi2aRPG0AgZ1sbEz+SHcgBGdfaMx7YvfiKNgOYt+7Jr8x7UvL5dmHhbl2Rsuc66blNfW52vGcOOtY9TV59pheftsPn9PLKQcwrfDzF4H8mlZCqJZZtiObpw0gKG9cZhNrPNmGci9x8HD7aeIzcSpEf5v2VXwuloFgGiU08tLaYd7Bs22TdpReWeR2tpoazSLi2LS5TXTtcjpkYuPUX+Z30bOpkGlfpUOgOwTRG/rbz5NwlFnHXQcEeZ5h0+a20bWrEKyysYoYWbssWkiYTsJLxquwWWsZBHroonRHyp0HdYgEs9TMboc0T5syVodMx6xOuq2Nl/nFTatCq8ar9Jpg0UsvyvfXAQGFT1+INzazbZ42JULwvWkytrHrvk5sHES/m0RHig6LashlfVWWDqmX1uFZNwRqRgp9/w95Kn9NnrOgAJ9bRjNsUzSkDuNXTdonsD63Y2njSSo01iEgf3Jd972CQ3++yXiVAMGkEo8frq3yjBJnHg7vasulSU0gQ3/v8WDgpHsMads0hepvUJGj9h0KTX8mz1XOpcKolMGWEGGkCiq1gmXapusQzO/orx43UxvTUmds41faBDqivSBydPq+8OSBSnk8z/vTdfnf2b6STCfTVykQTB2eiy/6wE3XZpP9gfCtjILN1Fh8JPr9g/mjEFTxh3sxAF9nn4mvReXfqbHi2iSUTzOhdETvpqKOWmKbDpBBm6JnVHKq3Z64aMqJThrnrNMts425jWd7Smnfah8p9jO1POrz48R3guih+tukr8IhgIqLABQFRRg+84T3V5VHqYudENd7hMZ4woHT1TmtqOY2WXmpnHMJCKDKC9I6RQLK1RthOzhQ81XH3xBVCyOAACq/GM35G6JlRg0qcpu0yw1Haols7gaXla8npzrT+xwn6TGZ/obnySeAAGoNBKvO5v986qAZhT0cCBAY9V/1XQpAANUKgnXcpQAEUKEQZE9yUq6eQDC5Bmt63ifP/QtAANUCghtOCI9tf2KlquPtgACqbWFMquouBSCAagnB3Nn8Ft12gwMBgtVOsoa7FIAAspLtb4jaQGBwl+IVIIDWqjy/IZoe1Rb/mkBgezYfEEAQIIAgQABBjdMPCQX9Sssuk2wAAAAASUVORK5CYII=)
![](data:image/png;base64,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)
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Question 14.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let ![](data:image/png;base64,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)
Integrating by parts, we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 15.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAW0AAAAkCAYAAABCIWsyAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAstSURBVHja7V2/k9s2FqZdx1fbPkNdcm0sattck9HSTlJuYoqzTWyr0Ozwzj9mVDix1p0niVOfnSJOmnOKKy+Zi11e4fVf4Jts/oFV/oX1Hh9IgCAEgKAE/lq/4o09EhcEvu/hw8PDI+U9ePDAQ0NDQ0PrhyEIaGhoaCjaaGhoaGgo2i1bHAVXw3jxbh/7voiDy0EUX0Ue0dBQtPsPguedATNdsx/5H/vR/seb3qPsPrUuOsHWdT9cfIKcN+c3ffAL5AFFu1d2b/bhcEi8V57n/66LouEa4kffrHuP+Xx6LiDe88SxjuE+u/P5xTbG+vDh9J0rhDz7cHZviJO9fr+x4aMLftFngx0k42Fndu89FO23wCa+90Myad54HlkG8eKy+hrySPedbYTL/j7yvafepeDF9OHDd9oYL+wYPH/yA054J35zbPKbPvlFX43itiEPKNp9WqUXuxf8wfYT00ShUTYJfnI1mSAyIN7w1e5icaGtMQ898gqj7Xr9pm9+0VceRoPg8XQ+P/c2jRsnX8nkg4iKjPfuOL2n5//a5uSk0Ykh2u5DnrXNPtYi2ga/6DofbfWP82AQ7dPoy1YNNTnwJu9bFt2kE8n7fZMDSNU9t4L4ehMYGlMkkEPVjDvbckLK6I8ubjn3d/2P0v55J22keuqIik1+0WU+Mi6O2+Ai5cE/MJ0FJEHX9wy7Lu4uZfxstE75oXBAkk6M9N83JIhvuxCU0igwv++Jq/vqSSf/002EVNzcTRQYexQE1+vKW0L7e+H4o21/8J1JlNNxe3+YFqMyYW99l2QxhnrvrfebOvwi4+Owi3xkXCyb5gLuO/AGr8vEmGPX0YNejp9lZZfxy70xuQPCCZUTLoQGqijG/vjLsrYAZJiQHgme13kwUzb50vG7ES4qqEl7zLGr7B5sr40Dcnsw8F6ni55BtLMdhCntQw/aOnxg2eai4lK0bf2iy3y4XFCqzAtb0WbYdTVFUnVRsRBtp6J11yY/3FQUZZp8dLdxyXvhYvzC2O8m/z87n+9eHI/jT636SA8Oh8+r9CGtbCgXbZ0I1JEWcm10jC1VW7gSbVu/6DoflAsHARbP61uKl41oZ9gddtmXaXYB8LM8UNV+wUXLcnU35aAhwp4El/ZZXqlsxXO5WKy7OHBhsxAGecwyDnlZUppmqlKeVIdoc241YzNFsTZnDTZnEmWYmdqUdwpV22oqNePKL3SRbNe4UP1dFS7WEe2ytIIpiu0QfodV8HMS7YIoR8HWLQBQTvovwuCD7HOr3LjtYqE7sKxyiOlCtGezneGIkF9Yf+F+8di/QcfsKPqoTbQ11+i24ovp9ALUrHOhIcNX8gMN4Ath4N/OOKf1s/547yZEkowPA2ZHMmYsT+8T7wDaG/jbT/bCrZD5mNgWax/qn1VtNeE3Kr+w6ZfN9n4dLoR5WcpFWT8NXCwLXAwnPyrbKokk6xBtXWoE8It88k0Rv/lfNPgdleKnHPN2Ycyb4Ze3tXG0e2+28x48kTQYBY/hyTCV6NrkUKsuFsKBpdFMC4RRtLPvTItHuorzKImKSOT7C5fvJ6lXtFcPWXVb8UXofwIThJ1v8MNqYVGjT36m7S7Ze044juxQmZD/5tElx+y+CjO6Q6PClLcXR1vXaHvJfeH/tm1JfnNc6jcGXy3zUaEiwLpfJdv7Ah9GLrKJbeBi6ZCLz2h7a3JRt2jrUiM5fuEjE37b1fHzTfiFKX5Hlvhp2/LW2T7nHdm9mOZGo6di51LRzj+rUoXRVGrEhWgz40KSrNYu8pyiAcZUtBNHFld4UyS4iWirUiP0ASOKRc6pild2cC3iqfOlzGGNmKXjKKYMVAGATVttpEf4pNygX3JqJONiWQMXyzW5OFRwYTVmna/vzOd/tvH1MtFWpUZy/MJC9J3ht2QZggy/N2LbKnGXx6zLr4cZfuL3cmrEti2jU5ZFxqI4MHDhYEXOv9keGlXNo3dFtG0XOetDidVI8GQlGpQmrSvRlrfiQiplJaeaOnbeRtr3Yptc8KWttipSl6MhOmkkbtL2ioeAZW21Jdou+iXysQ4X4sS34kKRwmA7ShUXcBCo5aIkHRJa+3r4VCXcZaWGcmqkgJ8UzWf4cVE14LeUx2aNn7S4qA5SbfAzRLvqyJgBwHO+w8mPkB+CaJOWmxH/QAzpq6RGmFPZXOsuN6muAuCibTnh6tohNJkeUXFlWsDl+7CHXljeD1JnbIuumlg6zHj/FLlfXQDA2yrZWtftN9oxrlEjLPPRCBdSP+vkwkV6RFc9oopimciLn0n4cTFnKa4EvynHjz67sgZ+8HeKnD7HT/q8DL/KUSMcGIGzZqtHuioOBq/TnHZ8WRT2qqmRbAtmda27nLZGtCtUj8C1wWj0VR1lik0eRIpcMQ4Zz+qIdzVlwg9hGf5k9LMqL1fATBGBqLDk9fvyoZyhrfpy2uWiXaVf+u19mpIAPkwRrwqXNbhYOuRiWXXMLkVbTHdIvrwS8eYpk+KBZXYIuGT+sgF+K59n+K3c0wa/StEuzWFn71zgk1lqWH66yzY1wvPjDdbespcnGeu0Nf0plG4l44334/NiasdVuVmTJX+MKzqWILouCrk4MQqHXBJ2cBru+9FiE8xUCwU4/2g0eswExNRW3a9cMPmNy35JfHxeIxef03tARCj1UyV0GRf/YIuRbVvORZteTw5Uos1rxxfTC4BdHj0X88rigaPcDmQPKH6KNIU1fmzHo8ZvuQ5+hU7kDpCKsbhVhHIUqBLhW7Vs+wFOBaVGcA1sIeB9zSy6Fbd3ph8RyHPh3kn2oMGZzoi2RvzoFiYBFX7Nhv09m2SAVUL2/TZEm3I48v4F/dbVxKserhG5WoThZXY/znNyLThvWkWweihV2L4PJ99Op/Sc46x4fxVm7JWkImbCNpb6AlwP7+Vg28bxePy30Yg8s2mrLr8BsVD5je0YK6RG7jI+RC52ptM/WXCxTLnID7E35OJsnVysK9qaCqhDETvh89/gEJLhl+Wuj2TBzvG7psQPnj6GMUMJX3HM23zMdHd0J3gfSvbIeGbC7582ba2INu1EabpBOj1OBpbVHNLvWNlf/n34LgUv2VbofuqqWDbHrP53LLBFanvgP9Hdy5SnTvEiy60o/kze8rh67L/gyBZ4ZFgelx1YqnPXKVcQnchbQIFnWqsK44vj/fMyntDGiJCfxT4k3P+yM5sNBcyOEsyu8T4nkQh1agkzXkNL/ANeIpX9fRAuPqjSlmu/gQVd5zeu+pXx8ZvMR8bFyw248NP63+5xkfn6f2x8nfEQDEaP5etz7LZXfBlEtIjf5JEWv8Hg3zr8ZsYxh4/E6Hzik69l/GY5fn+NK7SlPYg87ZbXvkY3Te9Ccf3CqM6Mv4bXBOyN/Zv+OL7BsYvj87DVy8T+pMuPEVf0m8Myv2nbIJdt4OJN37kQeQj84AvXPBjwe3lGkRNv2t5K0c7fYmh+nLwP7+BYx1y/bIm3p9jWspTbacDQ1m86we0p5iL92TzvVxqpOuaB4Qe14kr8Ev7bxu+tFO0qVvaDAX20tH5VX+dd2dGzwxbYakKukOX/6KPCAVlAegx/kaUh0WZcDCffIhdr43eswe8+xa/lV7wiUTapBIc/N9aNaJH85DpCuRUFV+QcKpSCbgXR3/F3D5s1Axe3kAtL/KR8dpfwQ5Iso+2281iubNNflkdDQ0PR7km0feVZ339AFLZ5m/6yPBoaGop2L4zWmQsnyn00+rDAKTtURUND0UYziF5w1eVrV5veLYg15WhoaCjaaGhoaGgo2mhoaGhoKNpoaGhoKNpoaGhoaCjaaGhoaGjU/g/Jl6MQGbafQQAAAABJRU5ErkJggg==)
Now, Let I = I1 + I2 …(1)
Where, ![](data:image/png;base64,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)
So, now
![](data:image/png;base64,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)
Integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
…(2)
Now, ![](data:image/png;base64,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)
Integrating by parts, we get,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= xlogx –x + C2 …(3)
Now putting the value of I1 and I2, in (1), we get,
I ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 16.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
Now,
Let ![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
Question 17.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJkAAABFCAYAAABZoETuAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAerSURBVHja7Z1Nb9RGGICnXAMnckgiZiUkyAGph+x4xa1wQM6QhOOmbKw9he5hFU3Fh7SqInByixD8gKQX6KXhUPWWSg1/IPkFIIF6KFUlkr9AW7/jjzrO2h5/rO31vodXCh+Jd8bPvN/zhmxvbxMUlFEKbgIKQoaCkFVzUYR8BTLxL7ci+1C7Te33202N0gNC2Ieuac5OMmQGI68IZUfcEEtlwlarTV1j9KW7qWimbNkSYsZg9AW5wt/2BoNLCFmWzTTYCqV393s7OxcRrvOyodPHVN94jJBl0mLkNTO2VhCo4WIKvkApf1PGIazFBu7s9C5ySt9wYS4gUCGQmd3ZJmkeluGn1gayxQbbm3RHv6oHsSandOUqJZf/uG2aNxCoqD2a+nRTmLcQMoQMIUPIEDKELG7BNasGqK4HISsAMngRGx19eZE1fiSEfRz3ICHpehCyAiATnD5qNMg76+X8kxSyKmq+pOtByAo0l5C0TQJZmfklFVFdD0JWQ8iCvpL757y1IkI2oZA5nSC/Ebb22gVM6OwBJeSEUH6YZ2kHIZtAyKBQb0H1xfaV6Omd/mbTYMzsCPM6mkuE7JxZAxkMunMSssFgLvhvkY650bpvaa5TQpvHUaWc4M+MEoQsRe6mipDJRj+phc7Iv+f+jhmvop5j1wrJoezjijCPzvO+DHnmGaFcPELIHNns32k2KTmGhY/KRIxLdAk9XKPOyU0kZPaipT9yUlTFv4qQwfdxTXsOJpN1zHsIWW4vuzvLGot7WaInv6lVL5mogzBKyPyf1+B8XWyJGX6FvPVHmeVBVpN+sjwgs30UegJRmTQ3CiG/6ikdDHqXuEZ+gZcCPz9vgOXntYASBl9ytbhcj+WXQVqDMeNZnvudZD15abI0+b58IYMWX9I8znpa4GU12OIe75jfqJvL6A10UguJnHfv4BD2u8qaoNQDB6RliPv+50J+jDLjRZ75sbOpkvj15AHZVpcte4GQo51Lgoy+z+qLJe1HL9PfGK80T/Y9st+x5WcmuE9RXcgSaESErLg9sjVowgaDqkEm/QxurINDC2ZHiK0ZhCw3yP7Mukcy0IjJ/RUAmZoqHZbNlqeEsiM4JeDfqPoxVe+UqIrA5eekCsD/jmz/lHx072+qNgGEvvSk5Y0kkIG2MnjroSwY+2p8aTcPEsB4sTde5MFVvODrNkUySo4gwIBAbKPT6sC7AlAjmgA+BzMCgdRBdGkjqryhCtlmvz0PFYGGxnehIiDLL75cUtJTBsDepXQfL/aqpZhgTkhcugP2VI58gIS6M/LBq8VaphK+HtIE8CyswlOouYRiM6hbf6gtfTAJWXw6IQiYXDjVDnD2RZJ31LkOoLW48TBsNoad4D1bsQmaSge8b5WaAIqEzJ+ddk3vhk6fpJnAA0NEIDBQSQomcQXqInH7AS6GRrWfg/tudtg9yIMF36F0SQJBnWoTwAh8suHRpXsSSHPtJ7PXmwUtJHvULUc/TSEdFihPkqXJ4vw5FTegbhIZvWuNXQiqgpG757oMqbKERZUqTQAj8MmGQ+ZkqO2WmUbjne2TiQUX8Dz8jEkye2nKO+6ogjBLE2aJnKrFadBvVm0CyN2xbBJ6HAVZ8MPAJkExOUtkKH92isBhXEVqIzBT0vm2tMhgMKe+T+G+r/eOfJABeJqm7brwpWkCKAwyx1x+AJXb7m/O235Bex4iwyjtqP7cycmTCd5aDxbgVQ5p3HgtR5OdWM79Ezuw4kstLtZdk6jr+veaRveTNgHkqr7hhEVN14FFOHkX2W/mpjGyPnuSp/qoluBUp/rIqYygIX0TK53C/2doWHC/PtME0GXLkB8LS57npsHAqWeG8Z3O9KdFJ0XTjkWq+rgC1VYklS6RsR8d5YWyBXbDZt1AO0OtrxbVIp5GQzFdPIgDDf4fmLRRHcTKQFa2JN1AGWwwZlZ9MqOM6tjayzDQkgRNCFnBkEECOGuwUZyTL+uNT4YBBg6568jHaTyELLNPqN7qY2euwx3lqo2WciN2fx7QrZQ4UeAFKNfpuljNa48QsowpDJm5HpJTq/JoKZki8H3m83c1431hHExckCaLqq1WebRUmm5U1GQlQWYnFe1+qEhNV7HRUt7hyHB/EyErCDIVgIqALOlYKa+5IEPpDCErADKvwyCmBDNqyNKMlVL97AhZyZB52qBEyNKOlfIgy+CXIWRFQOb4NXEmJ+NoqQsqLTiqY6XOQxbtTyJkNYEsj9FSqh2lCNm4QlayT3Y20lV7DkKGPlliyJKOlUKfDKNLJciyjJXC6LJGebJRjpbKMlYK82RjBJmdQhju14x6tFSWsVJpJukgZCVB9n8H73jdNsfa5RhB5pmoMbvZZHeOJLthj5CVCJltetiR6jWyssUe7UCPMs98Q8iKg8z1j1Sn25QtEDDk0cVrmrdvTJPpv8r4xbM1gaw7e42Qv691nq6qfg9c/aq6byYvk+Q0zNgUN29NEfppxTSvImQpIQOTMk0Xfw2bVDNco/F2lW8rqdxCUnrJ0OnBL/8wRb5+j52xGUWaQaodtPv9ZtXvVBbycq09gBwcDFjJ+7fTTSxkEjTRWYABLGnGUdVNZCTtuwleGuyTftpREDIUhAwFJV7+A13M4zWYJmQLAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Now,
Let ![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
Question 18.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Now,
Let ![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
Question 19.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I ![](data:image/png;base64,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)
Now, let
![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFcAAAA0CAYAAAD/qKSYAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAOESURBVHja7ZsxTyJBFMff9dqLcbbTnh1orzI4d9HSxHVjpdmCkElOTShIbrEjl/sCZ6Xd3RfwktPyGvkEFvoJ4DOg+2YBYWVhd1nIDHnFS8iGheHHzP/935tZuLq6AorFBEEguASXguAS3MmDBfiEEX1NcHMIl8MNAOvsVht2rcIugIl7r9VaI7g5BUK1+N61cPzPJAs5hy9FkTHxR+cZazZcsNsnvl8guDlGve6tC+GeHnO4LbvySMrmBsHN6ApGHUHT5fvA+CPOWCnYOePuT92lQcvZ6YryNwbQCcD2AnfQRXdAPnfOaFQPd2wGbaskfjnS3261vDWxBQ/Aj28J7lwz9mSTA7wAd2/GNFbBfb9GcDMEJikA/jJwAai1qlAA/myCM9AWru+fFMJZe3zre15BuuUjy4InTGAoD9RbmCOUEwB4VQnMsp5CzZVFU6FqCZc7/kHUkrlCnJpQjaWCG/Wai+xC9WXhGbbEw2G1sYPfg87hC2O/mZDnJvjwVHDDDhT6TLVc1ZJd5A/FspYzeOx7287AjunmwWtO2WGM/e+z6WFewAnRqO7avCLPEssCLtfAzHd1b+1lmXlp36+gKhaYZN/zgS+dbbXqUNbc5n5iuGGTBLrRm0wOlCAb7Ps09i6whJcIL67kDnPGu41MBLfvM19M9Zl5wPUdfqBkcUoho3KGtXcdBR/7oUlLz7jEt6xkuEi4Q/8NrCukX5z6Pu5+T5zQkkrCSOKbGrpk/TRwh/47Y29j5SUhunqwh6Hg1uubs1ZWWJJ/TFRzwV1mNyqNrGSRnpiV9frhWkRThwxmSEJquOjZUBJYpXaRJ5yY+3t5Rl6ysDC44XJI9qGrrLlDWYiU5ZnhDjNkUIquUuEwR0LrKRb1+vqkVYuJP26b/2MlMjDMldql7idaluFzcb8uLHPt9qDvoaB6XsHl3I+WvBPhDv+lsTC3UT3du/J/aX6XdMXXEmN3YzLHSnezeh8rNSu1s4EEgeASXAqCS3AJ7hIbL7OuEdyUUa0e2oG//DtoICFQWeFn6hyZAVtP2g5svKgJD+NhRWTSIRHtB4inb8KNQbudtTtFcGNi2PozsJFkxCBN3RXRfoDYaBGl0g8Tt/i1t194Vkw25cbotpMprVB9ZSAAia2+QRJTuwKB7krpFCdtYxPcpA5BNahZB5/YGbVm6G9NeNCEyl+CS3ApYuIN1WrSPJnworYAAAAASUVORK5CYII=)
Question 20.Integrate the functions.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Now, let f(x) = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEMAAAA7CAYAAAAguzffAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAK5SURBVGje7Zo9btswFMfZPd2bIPTWA1gvuUHBEm3WBrEJTw08GAaXBNDQQfZmoOkFOiUH6NzBOYFP0CUnsM+QlrSjJE4U89miZKZ8Bh5gyIZE/fTe/31QbDgcMrKFEQSCQTDCh2E+b6xFD6PfEp8/QuMnY3DTybLdaGH0BT9rNNgf4xV/o4eRWxvYFcEgGASDYBAMgkEwCAbBqNDStPtWHrBfFsaH3rdk2z3K1i48UHBkbv52yUBdUgtPLTzBIBgEg2AQjP8TRj6cjcVcMG5jsqjCZJUXRKUZo1F3R3I2XniBaQTTdC9aGFrAqdRZ874z3pfX3dFoJ/pskmnZ5CyZuMYEccDIOrsJS8YE484zQOjT0pqhhThu6ex9yDfpyhZKyq8uvXDCUABZLkKhmh0ScWj/eOl3u6cLanBUKrXak3DRPwutZsCu1f7XHD83x8/t9zTt7Amhj9eGgVXfusz16sJCIPnksRcrYJfLFSefury88OA8L0P7KggQyFcXfKz5Ba9gM2yc1WWuLYXFgLnclkPhkzAuNcMIZ1EcV/VakguGj4e49kVz6/W+JAec/37smrYENguaMi7HmFTmFYbRDWDspkyoPG9u9tm1q45f3vPgM7sBZNNwlfWICwZ27WgY93SRJ9Tq8MS6JuPJZFVYbTps2QhGCd0ojDusq2GfxvM0V2yr6ho8DJzeeYfxILjVbxxvDwYyTGxYSYDvdaTi+mEgNSOPb9sA6YF+N19ExUVa7ZqB0YB5WJgb10p+ejpJ0rrVBFCZbxCYVxe8ZxPME7gryqaHSp8sdY6mvuCgLnzXF9hXF7zXGQ8X3zzutjnb8F6B5oRD601wHuS5Nwmta11LYH13rSHOMzAp/uk8wxuMECddrsLPx1odM1B+Ebp2zIfCntK58w+vYTru63yvRiDrMIJAMIrtH5X8YYByWsQmAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Thus,
![](data:image/png;base64,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)
Question 21.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let I = e2xsinx
Integrating by parts, we get,
I ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Again, integrating by parts, we get,
![](data:image/png;base64,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)
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![](data:image/png;base64,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)
Question 22.Integrate the functions.
![](data:image/png;base64,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)
Answer:Let x = tanƟ
⇒ dx = sec2ƟdƟ
Thus,
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Integrating by parts, we get
![](data:image/png;base64,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)
![](data:image/png;base64,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)
= 2[ƟtanƟ + log|cosƟ| + C
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Question 23.Choose the correct answer:
![](data:image/png;base64,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)
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAxCAYAAABwK080AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAPTSURBVGje7Zo9T9tQFIZvmIG5fFxvlBkfZ4QJJRdBR6t1LC8FebAiS1AkD5Fw2DKgzogOfAxVy9CNoS3dOlD+AAPwB4C/APQeOwnBcYJN4uCQi3SEhIJz/dxz3/OeY5PNzU0iInoICAKYANY/wPhPhscQhoD1BDCEVdRyi3mQvhACl4brjglgbYDZjK5JEjnjKXYngMXQsAKQfQFMAOt/YKiZAlgMWLZhzKqWJacdXCqArepsQbPtGR3oFujlJQEsYpR1WAKjvCiARTyWBjNUoWERYVmaNmc6zojQsEAcNrRafut1OGSz7DJVlK+KomwzfXWhb1sj01RHGZAfCGzeKgHeXKdfyDdglxB6za8nYzdBaP6XWakMvxiAhn452DeHZXtrATZgkf/D7aOAwm43Fum1XZDfYZo795KgMCGKWlajlP6t3yOFE9VypkvWPEDOXol9JJMI12YzlLLv3cqsuNMUf7AABUrINQJCS/OwNm2KH6UL/pn7MIvzcsCIfGo4znjH13KNMZnIv6NqrAcrR9f5rzsK+lbYpqG94TJ0EXbNnuhCky4y/SMWk6xW5JtbftNLYK4G7zB7COh77a4JUn4nDGbXYSEQnWVXebpfoSZkCL1Bga/rIj8CeHOoY612OClgHghCLrHoMNudafs50DeeZSvihGOp0zLNnEoK29Zsd6pSMYfZJDnmxWI/seMdB1iE7OrYh0WG5Rjj3u41LMZxzJG8B+z5C2zl42rhOOoEB3asOs7EY3vQbIF8Txku5j0HVpDJQU0oaxrmiyucd7NL8H1cwO54U+H2Fqie7Vwi2h3HWMCCBu6paNIG+cOBY5rj6G1wvO2XbHcq0Yob8UgmBew2Tjwuw1wb8O+SdOZrmO9tku4N42iYDmTPO5Ka++6pKp/okawBCy4Es1BnbDnJ1icOsGr3ckcmc39U0xwNA4UekRnl2USBVY/kOZnMH2NbgaBKlvp2gdJvlNlracmwWlvmt0DyaW2tXvHgUqIDbGSZvdwT0cedAUpO/ONKr2rWIvGuwdss+BmnsOCEV5Gko0Z5kSTlKMp6Uz2s68t5mIgY87CAjcgIYC2ANYw/bny7QG+oXPgcVlkEsIeeK+i77rEc49xdAAs4YrQDWd1+31hVqtOH+7Q/N+w5sFbGrW5OBbBoH+SN9KdWU0gBLHxKsJ+0a381wErWvEwJ/BOvPEUAhkNALAKdjEQGBpj3GlIOVtL+gkhqnD4KfVC3Bv2N6jawwIRc0Wxsj/CJUF6CnUHWslaZtV6doDZHFx9ovApg9QFbixh0PRNCLoAJYKmK/8+nMTLEg1FjAAAAAElFTkSuQmCC)
Answer:Let I = ![](data:image/png;base64,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)
Also, let x3 = t
⇒ 3x2dx = dt
Thus,
⇒ I = ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 24.Choose the correct answer:
![](data:image/png;base64,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)
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAZCAYAAABXTfKEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAP2SURBVGje7Zg9TxsxGMdNZ2AuL84GnTknYzuh1GnLeEIXK0uDbjghq7xIN0TiwoYqyt5O0IlPgKoStg40X6CVgC9A+AqE+rHP4bhckrskakE10iPE4fPLz4//z9+Hdnd3kYl/EwaCgW/gmzDwDXwTjxG++JkQ8Sz8LcOA/EvwGUGHAnibOMEKp3gTYXrq7u1NGphdydmJ6P9Glp06I+8QtpoODxbSTuh/gO669vS6U3Awxj/E37cyMPlpe/6LmrdMSJGvjQzf9yuzFrJOK0Ewk6Z92bLqads+FpBZ20voCLUAtsP5kv5fwJ0FgtClaHNHWP3d0PBhEN93pxil7ylGpyA9g94RO25hZDWfCvwgqMxkSSwJvoi3QYoxYftJEiyVApHLeJ+ptUt2UiFvxc6eQyeg9xiXjvtNEjaKzqMzMfCV7ftzcf2LaeNE0vjxthl0dyLJJIwbfuCQFchqRNhhvz5J7vWX+Mb0hMZoYUMco2ulXfhm2atZWTJob8+dhNMBGSEnp/q5pjxYgv7LFj7o6CJkjVU+cH1/So/vULIJJ8aueYuM4H2ln1az3zwArufZhGD8DVnlr/oZL5I1uZYU5iALfAkVoSuxrhasq287wnYGup2aZy8KnWjm8vQzFFQJcR41ECkfDXOMywQdQeZHF6Of6YItXZPYIFxc34o6Ktj0AmUfAFjA6ZIAeNNvHvJkhpupE4YRspPWGGSGnyLrU1tNKKRyJyOdhdLRGHaAOPzOiQizEDJT1YWHYBPfg3nM08ag7OWssCr7EyelX0YmyZ/v23MCfkPLZC9ZvJ9jdyEdCn50wXpSqph0F4tRMj9qzUJ5a6kMGg/8zganaBuesttYtLuexZKvMx9xwgZt8ED4Hf0SWum77ixYp1wO/YYCm+XYpoEvNZ/gT1ADQFY4X345zsyHEEmzlbTp45KdscJXdkgWxjbK5X4pzVd+dZRLUk+IkeKXpOejwAf5pPn8R+gzjR0eVvPDU3OXdYye8OMdAXjh66vDfkKIS5kGLYrr9sO7gIKvNzor/Oi3Jpgvr/PnUaOQNoGywA8LfFvM6cx23emkOcF6qRO8SiM7l7A4uA6D3oPzKWF8jCnfHDbzVXaEzgOgKIlpyXHEhKWtVVayDZLHGX1je56l7gfqPXW5s+eUrVN3hkSZCd/XMiDHFuMI+2klWb1x+PzQqbWhuGtuEIHrzoDTKlBeTVVwYZcIRufak2u7OdKNUWX6NdQODYXTQlXfIeBWyANnQd0JRA2oVKrh/eC2czfYYCUB/uL+GbmIw1EQxPuMr0YzE8bpdfPs7d3J9yy1YoPRUh7jk2iBxjh/Moid+RL5lD4pmzDwDXwTo8UfUJ0zAQ4WaI0AAAAASUVORK5CYII=)
Answer:![](data:image/png;base64,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)
Let I = ![](data:image/png;base64,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)
Also, let secx = f(x)
⇒ secxtanx = f’(x)
We know that, ![](data:image/png;base64,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)
Thus, I = exsecx + C
Integrate the functions.
Answer:
Let I = xsinx
Now, integrating by parts, we get,
Question 2.
Integrate the functions.
Answer:
Let I = sin3x
Now, integrating by parts, we get,
Question 3.
Integrate the functions.
Answer:
Let I = x2ex
Now, integrating by parts, we get,
Again integrating by parts, we get,
Question 4.
Integrate the functions.
Answer:
Let I = xlogx
Now, integrating by parts, we get,
Taking, Logarithmic function as first function and algebraic function as second function,Question 5.
Integrate the functions.
Answer:
Let I = xlog2x
Now, integrating by parts, we get,
Question 6.
Integrate the functions.
Answer:
Let I = x2logx
Now, integrating by parts, we get,
Question 7.
Integrate the functions.
Answer:
Let I = xsin-1x
Now, integrating by parts, we get,
Question 8.
Integrate the functions.
Answer:
Let I = xtan-1x
Now, integrating by parts, we get,
Question 9.
Integrate the functions.
Answer:
Let I = xcos-1x
Now, integrating by parts, we get,
…(1)
Now,
Now, substituting in (1), we get,
Question 10.
Integrate the functions.
Answer:
Let I = (sin-1x)2
Now, integrating by parts, we get,
Question 11.
Integrate the functions.
Answer:
Let
Now, integrating by parts, we get,
Question 12.
Integrate the functions.
Answer:
Let I = xsec2x
Now, integrating by parts, we get,
= xtanx + log|cosx| + C
Question 13.
Integrate the functions.
Answer:
Let
So, now integrating by parts, we get,
Question 14.
Integrate the functions.
Answer:
Let
Integrating by parts, we get,
Question 15.
Integrate the functions.
Answer:
Now, Let I = I1 + I2 …(1)
Where,
So, now
Integrating by parts, we get,
…(2)
Now,
Integrating by parts, we get,
= xlogx –x + C2 …(3)
Now putting the value of I1 and I2, in (1), we get,
I
Question 16.
Integrate the functions.
Answer:
Now,
Let
We know that,
Thus,
Question 17.
Integrate the functions.
Answer:
Now,
Let
We know that,
Thus,
Question 18.
Integrate the functions.
Answer:
Now,
Let
We know that,
Thus,
Question 19.
Integrate the functions.
Answer:
Let I
Now, let
We know that,
Thus,
Question 20.
Integrate the functions.
Answer:
Now, let f(x) =
We know that,
Thus,
Question 21.
Integrate the functions.
Answer:
Let I = e2xsinx
Integrating by parts, we get,
I
Again, integrating by parts, we get,
Question 22.
Integrate the functions.
Answer:
Let x = tanƟ
⇒ dx = sec2ƟdƟ
Thus,
Integrating by parts, we get
= 2[ƟtanƟ + log|cosƟ| + C
Question 23.
Choose the correct answer:
A.
B.
C.
D.
Answer:
Let I =
Also, let x3 = t
⇒ 3x2dx = dt
Thus,
⇒ I =
Question 24.
Choose the correct answer:
A.
B.
C.
D.
Answer:
Let I =
Also, let secx = f(x)
⇒ secxtanx = f’(x)
We know that,
Thus, I = exsecx + C
Exercise 7.7
Question 1.Integrate :
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 2.Integrate :![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
Let 2
= t
⇒![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQUAAAA7CAYAAABykZ/4AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAXjSURBVHja7Z2xbtw4EIbZX8oUCRC6c5POVlwaSHFYC0ZwdWxhqwSpcgQOqQPZnYGDX8BdyjxBDrg8gd/ARcrr8g45U7Yk7q6oFSVKlFZf8RexN+aKQ36aGc1Q4vLyUiCEUC4mASEEFBBCQAEhtOtQSNPl80iIH0KIX5uSP2OVHmBgFFofF/JT9RoVv+Ti4yeg4BkKh+Lw32WaPmfxoSnCAigABYSAgquUOjtYLKLPUoq7bRMGFKYpFxsDhZlD4SKJ3ggp7/RiaRJvdYVCquKDaKHes1HHa2OggKdQLpwBoHAeiS9zXpRTsDFQAAqDQSHPCPdpFFvGecwCCkBhdlC4uvrwJJby68aGiM6/9AEFvAKgABQm4ikMsSiBAlAACkBhI3QAAEABKAAFoAAUgAJQmAYU8mvuK4cyByjox9hSyDsfJfRAYYZQGN1ijs6vy4UtfoZckFOEQglVP301QAEoBJVaLo8/XF09MRekeBF/N38GFBrANVtz8hYoAIXJQ6Hy+oECUJgaFLbFvV2gkLvQegxdu5DE8TtfG2QKScbQC7KpjYHCzKFQbNSGPefdy5zldTaGPLw9U+n+XLyE7ByKvZObEF6Cq43dbNn/GRqzg0LVYRBRcvFm3NQeX5fkOhTG1hWYRFG6a52lXaGg+2Cs5d+GNzNFKKTqbP8k2rsxYSzlq29nSh1kTYFRktZ6CtmH9GlG93fPsS+cKUBh6K7AbZ2feiGOGfRTDh9cu277hoIOi3NvWD95UurimXmjOpTi1hbCbbqWGgoBk1C75imYMXTfUKjr/NTfwfyd/jeA8AcF167bvqGQez+2MbI+oBfiO1AIAIShoFDX+Vl9TmD0o22H6RwrEdfzISZQ23Tdusyj65wXidwt+zi7Jhl/Xf8MUJg4FIbs/AwBBX19OibOk8JLtTw24+AyZi4rDR+eKB39pcM2vXlVEp/m7rJ2pX2t7S5zn62JhjZymfPCA2iQE9SfXUSLz0BhRz2FoUKUoaFguuUPcfK9W/y4mYoc2FqloZk43ItObuJEnZp3dN9hU5u57wsK5Snn7ROvraFQd3T1EEdZDw2FJoeRAAX/Ntbr0dzE2c8MT6G8M65ugioA9FXiPSooFGFOACjMyVNoekoRUOghNMo3/OPd3p5Uaw4F36HVOKHQLmcEFDoAoikQmiwaH15XH1Bw+V59PclQydHbYhwp744S9XaXodB1zifvKXQ5R9AFCr7PK6z6TBco7LKn4GPe82SiLZGHp9Au0UhOoef8AlAYwDu8h0P+FMFc8EDBsjcb/H3d97O+hwgfPIURQKGfnML6I7N8YwOFZt5C3f9Ti+h9lTexEY9Q5tzOW2gChT67Avvs/AydaDRrCx42e5lEM180vAmK1U3RtKhniLnvEwrF/nj0qvRjWbPp70KpZ7oE2vY3a8MBGqLc4mV70meYtw331fkZFApx8k6p34+LWn3j2qrmV8ZJmt8lzfneWN+eweA6931DofAGkvj0lZTfVuYja4iyf8fRegLbofD65VPx9L/XafpyDFCY6jyiMPoz+u1ayD/+GeN3AwqecwsIAYWZQ2FbPgEhoNBloxuPnPL4zFbJ1hYKLmOgcPYFCkDBmpSzVm61gILrGCicfYHCzKFQPHqKkzTPCOu7SplF3qzjdoVCmzFQOPsChZlDwXaUla0Drg0U2oyBwtkXKBA+WPVQhNLdU2gzBgpnX6AAFGrdzqoiD19QqBsDhbMvUAAKVrdTiuqSa19QqBsDhbMvUAAKFtdSXtsy076gUDcGCmdfoAAUNrSt3ttH78NcTyaegn25fqCwouydBFterNEVCk3GQOHsCxSAwkqcWfUqK59QaDoGCmdfoAAUijuI7p3fXEhn+1EU/71y2EZLKLiMgcLZFygAheyATlsZbNUZBG2g4DoGCmdfoDBzKKyc2FupqopGNyi0GQOFsy9QwFNwj01H+oJZhIACUEAIKAAFhIDCKKFQvlyUGBWNd/NPLbmK4RBCQAEhBBQQQg31PxGoN66AuQuxAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 3.Integrate :![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 4.Integrate : ![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANMAAAAtCAYAAAA0n16wAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAATtSURBVHja7V07bhsxEOUBfIAYENX5ABblMq20MHyAWAt1hitjgcB1sHYnwPAF1Lmzi9Qp4jaNbpDCN/AdEpFrrujV/rg73I/2FQ+IFVkezszjDN+SFLu/v2cAANQHnAAAIBMAgEz2RjL2DwBsATLlkAmzH4DKBDIBIBPIBAAHRyYECwCZHJIpDC5PPD84RyC7gcD3zi+D8ARk6hmZwnB5LIT3cL1aHSGRu4HV6vpoPhbrZRgeg0xEkIk+4WzDGH/3gvCUmkwyaB7nLxSffeeLi1hOFYsnkKJm7APvlIvFI8hEhIVgTzpBhX93QS0+KAIQJL4ZePVvxt757OYWpKgf/7pxB5k+qsZMzH5QtV9JMlFWpWC5/GraeTPjt2zkvaJ1JKj2A/SjmxaPTX5T9c2pVclRoIaaBC5yQDD2NrTq5KZnZpONKzKpFtLR2kZWJrR5hK1+D9agUoGU63uKuDsiE/9L0YYlyaRnPBcJrz57PF+3VZVUi8nEWx+UsDK2NjEe+WgkEro+BCQ+2dhI85GN0e8OjkxaeXPRPvhChG0lshY/+kCmsra6jJW2w3w0siOWnQ+1nYMjUzST0MjtyRmqrf5+9xhBzpDdJpONrS7V0SyRS/9Nm1j2gEx2A8ojkkmmSHKnTTjpTNOR8mdb2+ustRaCP3LPD70Re22CTE3ZGlewBtdNB0cmyvJukklJ4jlB1Osp8zyLdNDn1z9XNbNn3sE+oasmqCKyWDxmja3KmNqyNTMeDaqjZUSPT+us7RpruRRXJpnq+LzzZNpPrOwgykDHD4yNIEY2iTdX+8aqJKgcz5RPn+VY8hKUekwubU2f3NxX2yC4PFUEmXo/84gbC1jb6irfZxLL9ElVn7P8WTodecFwTqaCmW4X7MgGyoe8lAkqWyZtU1GCUo7Jta1Nksn0S5yb2+qZlR+KIIn80Xmf9EkVn3d+zbTXg5doG8xATqf82bW4YJugyfeXSVCqMTVh6+f30QtGaX8r8M++RSpj+mSfJYjkrZlsfX6QZDKdRN2z21TwNB+kbQQtm6C2Y2rT1iIyUXVCqaJHim1ZpCkSIGx8ftBkGo1Gf6iUGqrZvlwSpScqxZiasrXJyrTXyhGTqazPyWcKqudMSVncpgdXNnDvJbgLvjQR0LrbkEq1eURjasJWm/e5iEXahBtXmITal9vmWfqcvjKpja580xaZTOWpqPT3hUyUY2qKTE2qeUnbitY/pj1ZJKvi81bJlHe3Q+qBwIIgZjkzrrrbGcuFPO4yQanH1DiZHDxnkpK2+my1Fy+IVUb1UDnnYKLpMy2Nz8V4HXddH69X9bmT2aHM0eWiG4fS/i/qh7NLrXkoUTtiv311sx3JVYJSj6lxMjnYAaFyzCSB9A2f/ipzH0gwE1da9RuL+VqqgNJ/Z57/XZO+qs9JK5I6w7JcXhUdDtREySNU2uuu9uYB9BjiyWXyftUm2W3J5HonMkCHIcaqfQMsyOTyPBPgQFXryfmsgyJTkjh5FasvJziHjiHGqRtGWJBJbzYc6t1sfYBu+XEHRAeqUx6Zhhqo3okP3HvB7UQdIVPh4hatXqdbPNyb15FWr8xF/eaxAABVCWTKqE5lyJTc7gF0ZK0kxAPuGu9QdSr7FTL4FoxuAd+C0TEy4YvNAJAJZAJApo4ZBDIBIBPtugkAQCYAAJkAAKiD/0bFqLAoFChNAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfAAAAA4CAYAAAACYKqLAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAmZSURBVHja7Z0/btw6EId1gBwgAax0PoCtdfnajWDkALEXrl6QKhAQpA7W6QwEuUC6dEmROk3a1/gGKXID3+E9U/uo1Uqi/lAUOdJ+xdc461hLzfA3JIcz0cePHyMAAACYFwwCAAAAAg4AAABHK+DbLD1LN9nlHAc026SXabY9w7gAAOCoBPx2k7xM1tnrOQ/qdRJ/Tja3LzEwAAA4CgFXK+84Tr+/ubt7MudBvbt78ySN4++sxAEAYPECnoveSfRrKStXtZMQnaS/5h6MAAAAAj57wdtmV6fncXQfRdG/OfH5vemsfru9eZZE0R+20gEAYLECrlffUXL9Va54p2dxFD0U4l3CJNLXSfSVVTjYBIZX2faUsQEA8QKuxVHqalUHGHG62WoxVpNuHnTkk27y52a7fda4qxDFD5yFQ5vtJ0n6qWxXOzFvtikAAFEC/nYdv/ctdOpvxuu373tPsg2Z8cXOgeHZdWDS9+/AcaHsZ52sP1R3aCQHtCpg5d3BUYmkYJsX8RD5VrNhxaHPkstb1koQD38+XPyHCLj1s+ttd4dHA01b+DAtIVblCDjg9zL8HgHvWIXsVrHmLUP1mZ1QPg5s6Ux5t0Wd/LE5L3Qh4F1n90WQ4fAcHMdavoDnti40HwQBR8ARcAR8sMjthX6XNDb2rrULAd+tlM7vTYHHfpfA3XlmKFGB6cmyq7P8/HuV/pCa+IjtMe6MPQJe32busUotC+JqFX8bs8XoQsC7Kq51nZEj4FANTotjouT6s0QRx/YYd8YeAbcScMVu2/xwK72PWPfdNukbFPQJAKYScJxquUKebS5e6euKEpMfsb8wY864Y/OLEfCTk5N/xk5wY1bgfeu1uxbwsY5cBD8KwXfuj519zQF5V8kQkvkJOH6PgE83WQ04J9a10rPb7OlYYbQV8N293c2274qqK0HPlyPnY5dcfy4LBNfb5NJ2u4HJDAHB77F5EQLeV+SU0K/i1Tf9mbGrFBsBV5GsdoZDJ7k6LRfjqAUnjrLQxwh4dnPzV/kZ8mMFqsSJRer7QcDnNeb4PQLuabVhXk0XldAqglucbT8a5NCrZEMFvHw22UTT/1UIuKNtK5eGRLMVuZjsXfpkpoJqU28A6WSb9FJqxUT8HgEXLeBdldiKO+Aloawnpg3bTh8i4Eq825Pf/FRic2lIrgrZgD35zo0K8PLa59mZFm91u6Fpp0fyZNY3L0QyXbdKQo03fo+AixZw6bXQR0W7QhLYajsDz198IQoPv9J+kTz/crCTE69+9lnFKvFXvxtH8W+fK8cmG9S5KXO3p7G1JaSLB36/YAFvumrlS1Dn0I3MLqJ3143MpYBvkmQbMjlqZ2uyErRUEZX1OvkQx9Fv6SuUsWWEXU5m2nelBt9DWgAXQbegLWaX4oHf2/m9LwHfB+X7o1oV0KvdOVPydC2S1lt6vgdZl0VdSgcm1xObKyNSThRyspV4RSq3vTj+rZxY6v1rY9AbWMAln6natADWwZGUgAS/D+/3Uwu4PjbTBZyy7PZpOcAoAtCGBW5zZB/AIaVH8lbG4bgGuotnKhtpfm7pcbyVfe1XQ/KCNX1fdi5nhF3Jn1MLiuSdM9sWwMW4CglK8Pvwfj+1gOscL9Pfb/MzMQJeRGmcpU3iyM3V6IY705gkmDw563FCdXk33uWzIuDD7NB37oqPFsB7O5guKdaneB+b39teD3Yl4LZzTpfmmrRRlIAXjtezUIpUsnXy2uWkVj3/nqrF6pSOrO/QN937l9IydikCrsZ4k168228fxw+m2urK3/aro/ihK5O8bIdtt0emeKc+WgCXA5Mhf8uHgOP3yxLwaoOurs+uk/UH8QKuHYj7pGYB1y/UdYvVqRykXITHVLhHQsvYJQh4Mb6lMSyuQVb8uipUynYPzoybtuxKdtglhK7fqY8WwOVxGXI04GsFjt8vR8D3gYp90GUt4EMahHDvcLhA9zEg1y1Wp3IQtYWmn6mt8l7olrFLEHDTqlj7a/m7NQlwlyhrW+xbQdHlO/XRAth2IWPzbPi9DBsJJuBFYl8AAQe34t3mzK3Vrxy2WJ3CQaqf75r4Q7aMnbuAN62+a5PF//9meg9a6E3jrm1xyFzh6p36aAFcfd6+57VDnq1pkYPfh7OR8AJunxeAgM9gFd5lQDYtVvsa45g2rOVGCn0d2fb7uGgZO0TAJexAVQW8zX+bRGnICr4m4BO3AQ7VAvjQRpvHweWz4ffhbcRWwJ2M05xX4H2//JIY6sx9fs9Vi1XXEWY/A687dKiWsT5X4C7sZoiAm5KI8gS2VfpDfb4o7dri/2MEfOw79dECuI+Au342k9/7GNOl+f1Sk9icCzhn4NNO6n0F3GWLVR/bmJ1baQFbxi5mC71hzEyNddSNCT1pKp4n7aU2bQTc1Tv10QI4pIBX/d7HmC7N7+d2jazQ0R4Jk5s0/bs6dmyhC99K7zoHc9liNbQjh24Zu5wktvp3aLqznX/fgUVYamfgHtsA+2gB3He717Vf4PdhbSSUgJdX4W2/Z7qaXI9UA5VShWZn7spEddliNaQjS2gZW5zBzaAmf/mubNmxyxPCxSZ7dfCzyvcqd/mr7ZoZuqENyUJ3/U59tAC2Xci4EnD83q+N9PH7KQVc25uuxaB2wMrf9zbLnuaFcEzBRW3AAjQzAbMzt59/um2xGtKRQ7aMNdXMlroSb3reasavrq2sx+0i3bwzZqYPSLyp3wP31wbYRwvgAwH3fA8cv/drI339fmoB39tsermK45/V7oRtAQyCOQMRZzxgCtoSu0wTUd9KbHPGphIbPr/suVjss/GCEHA4Prr6Dmyvrs6aIv+QtdB9BjahAhN8HgFHwDEcgFaKZLdK+0K11ZmXAzaUMp5LN7IxhO5Ght8zDyPgjauOq9N944ZH4vP7udZcB+xyLFZnbk39wAW2iLRlaW2NAQFfyCRpTtjBWQG7tJvMliZ4eUDCNVpAwOVF1aonrXZMterR122WtIIA7NL3ZNZ1nj6r9zFxUxBAwBFwi1VOU7atTcUlgGO2S9NkNrTamURMxTIAAUfAhdLVPhEAu+w3mSkRn2tOSZ64RxAPCPh8WGoWLWCXxziZASDgR8QugYiysYBdIuAACPisUOUmOfMC7BIBB0DAZ4SL2sUAx2aXCDgg4Ah4UNpqQANglwg4AAIukCVcdwHskskMAJs/uhVOU59jVTwjSdJPVF8C7BIBB0DAhaH6A7f1PuY8HLBLBBwAARc4SZomyKEN4wGwSwBAwAEAAAABBwAAQMABAABALP8BYRdzGgx6MXEAAAAASUVORK5CYII=)
Question 5.Integrate : ![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 6.Integrate : ![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 7.Integrate :![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 8.Integrate : ![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdMAAAA5CAYAAABtVsH9AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAiWSURBVHja7Z09btw4GIZ1gBwgASx3OYCtSbmtIxg5QGxhqg1SBQKC1MHYnYFFLpAuXVJsnWLTbuMbbOEb+A5Zc2RpaA31R5EcknqKB4gn9oAiX32v+In8mFxfXycAAACgD50AAACAmQIAAGCmAAAAmCkALJerInuTJMnvLdnlN/oEMFMAgAlsyvwkzS6/NP9Okvv07MMn+gYwUwCAkZTr9R/vb26e1T9/OEs/JUf5L/kzAMwUAGAC25QvZgqYKQCAPmJmSpoXMFMAAE02m/WL7Pj1V2algJkCAGhSZNlmvdm8oC8AMwUA0ECkd7Pi6o3XwS5JfjNWEZiWp+Po7OKhH24StBWqZsSiI/k9qfjZR2MN/T5D65gpZoqZoq1INbPdCrPXtuzOx3QvZoqZRmGmBP642S4+SZI7+QYQs5Wnn6f3ebk5QVv+c3Pz/tnr7PjrbjzT+zQvNqQHaT/9gJmCgwB8mSXftsFX2mtYlZvL7i7KzUu0FcY45kfJL3nMijzdiL72/b0oZoqZRmumCGCpgbgKvNuf0/SH6RlprS30ZXEM9x6IqmwDQfgwbUfrmCkCWBi71G52t1ql323NZggwboy1LF69FTV3MVPMlHGcaKYiGJ6mya2Jd1xzLtz30yg4LWNE31gsLTf3pvJ5/HxoW22iopB9eZa9w0zDbXtMWg/KTJv3XgbekeheuO+nUXBaxvANcnR09K/NADznpvJ5/Hxo22WWfpEfpknzhtv22LQejJmKtM5ZdvbZxGxizkX7fhoFp2UM3CBp/qO8Kp9X70/Nr+KNWV+Hblsd1ORZAmYabttj03owZrpN8San/5jYJ2byon0/jYLTMnb6WaWr77V+msBseO+h6XdIPo+f67apjBMzPWy70XqIZroNfqe3vpmp76dRuGhfWeTn4l22r/1QrwJtt6/Z2P9wk5jaHmP6hvJZX67b1n4A2pQXL1dp+rN+p1WWFydzx1F8p9jHmibpfzayFrGZKVoP1kzNCNzURft+GoWL9smVZny9EeR37XUb9yvkmEn5mryhfNbXodomFhxVhpreZ2flu90K7fT+VVG+nX1NFgt5YKZxa93FOO4e9qpV7NuYlq5+XpTlifDILNsvYGLNTE1esO+nUbhqXwypNh8DjM/6ivUklt1+ZMwUrU9rm81xrArPiMV3D3FWrGIvr543D5jlxUm1y0W96th7M/X9NAqX7cNMl6WvEE5imZ/JwEzR+rS22RzHOrvWFWObh8DxZprcH2pLTNs8fD6NwnX7MFOzN5PP+grlJBbM9KkhmL430bp+n0wdj7F74+vdCu3f6fxCk2aqUwT9UKdRjC3w3dc+U0XfRd6+SSukp7fr9dON84cqLu+Tmer2wSH0ZUJbsZup6KMif/Vx964q3RaNUAU3EdSa++Px3e4Y3di6b1yYaSix1KbWbZhpuwzq0O+qto86MdO6Aa6LoOsIwFSB77nXW98cQoDib2VjlQUSQr/anmEsTVuxmqmqJrCowqSaLbQ3+IuV7vJiEWUaTtKNDc24mpn6rnfbWrdhpvICO93Jh7aZ9u196vrcZRH0WSIwVOB7zvVub5ZWAKmf4tptmduv6qdDNS5SzEP76roCzJK0FaOZVjrsziLI/VT97dMZjOqzoYcwk5rRMVMdrfuud9tat2KmzXYwg2Y69M50zAHFfRfrqgi6CUGYKPCtc71dZbX6BBlKv44JLLr6Wpq2YjJTVQDeC3SP/yfPfGTjrE23L3bZ1MyU4D1X66Ho3YbW7Zqpfvpby0yHnqqGLtZWEXRTMyzTBb6nXm+XaQ493bkoLm/bTOdkPmz3gQl92S4e71uWYayZNsagMlPJNOpAp3rf2jWzHdKNjmam9LMqlprQuu+x1JbWVX0ydzwOMjMdk6IYIwDbRdD1b3DzBb6nXu8cMz1Uv44V8pin8T59oS0/x1FnnMeaqWom2pxstcr/rtcUdP39GDM1oZk570x1tO6z3m1q/dALkCaa6fh9pm0RDAVJV0XQtVKyFgp861xv87TZWkTRm+ad0a++zmamBpilaSvKNK9izBqjbd0PYrZTG4ngOOuvnqNM8xrUjGsz9VXvtrVua2tMEwdHHANX5Pmf7XSwMg9/mqS3c8y0s5MdFUGfm441VeBb93pVaa0+k/W9X00aat/70iVpKzYzlYNZuz9U2bJt3008l1O1zcSkZuau5o0lltrWui0zlWenva8BHx7ilKn7uWbaFsHQ6jMXRdBnP1EZKPA993rl36vTWE/2bbUWY/jcr7bNdGnaigF5X2QdmORgVtf/7ao4I9eB3suePJ6P2ReEbWjGlZn6rnfbWrdlpo3/PW5BFJkOuZ1XZflcpK+7vlM5UK+Ps69Tnm7GmKnLIuhzMFXg28T17tpSDWy15+6hHXnxsU5nhdKvpgxVpa+laSt4I22C7f7rA7k2aj1ust77vmPKoh8bmjGxzzSWWGpT6zbNtGl/kZ83DwBPCt13PwTsPSlm6/U7ncPBxy4qAdANMGgL5LRhV8WjriAagn7Qujkzdd6udupA94kGEYCr2Sksm67aqM3/X6jTiKHoB60HbqYxXyRwE0E8NAuVWkdkVQUC8vO8KM9D1w9aX7iZAuxmD1KR/sdC/V1BDhjXqWi908KgMFPMFMIKuN2LQ5Za1J1xJQgDZgowmmbZ/uNpN/Vspt7yEONRYoxrGOOKmWKmmCkENXtRrbKcu8ANGFfMFDBTgOvhI7KAccVMATMF6KGrkg0wrpgpYKYAI6kWr5zeMitlXAnCgJkCaCJKxLGSl3ElCANmCqCJiZqlwLhipoCZwmLpq6EKjCtBGDBTgAG22ymyYkNfMK4EYcBMATRnLqpzJcVG/yzL/5p6KhEwrpgpYKawKMS5q31nTfL+lHElCANmCjAQcLuCbQwHlTOujCsAZgoAAICZAgAAYKYAAADR8T/DZt85gNx8cQAAAABJRU5ErkJggg==)
Therefore,
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
Question 9.Integrate :![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIcAAABACAYAAAAwCmQGAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAQSSURBVHja7ZwxbuMwEEV5gBxgA5jucoCETrmtLCxygDiCOiNVICBIHcju3OQC7tIlZ9i02/gGLnyD3GHXlEKJK8myJdPUUPnFALYaieTTzJ8Zimw+nzMYrMowCTDAAQMc6aAY+9tHAxwG4cDbDzgAB+AAHIADcACOU8PhyrPOAnGTiU5x9wo4AEdiceRfcnH3kv1m7JN7D0+AA3CwKAx/3i8WZ+r/g8ef2MD/0K8Bjm8cVkohBnAAjiqTngNhBXCU9UccnovheEnFa/QSDlfT2ECIOIzjc2QrgKMUTkQwuyE3l4CjexGq6wz5nwoogKNjj1HuvooNlfACMWpSUDK20RdaeoT/r/NPP4ovnZlLwGHOFov7szvBXhMQtHpFWiIXm0kUXzg1l4DDPCD+gH3I55DaIfnP+btLHgNwWAkxYjMa8TeKmYgzcMjJvOJsZSImUxGjWbeVUDncSTiyOP3livsCx2Aw+KOEKeBoGaM94T2beLuopLFJ+53779Es+pHqD7eyFDJwJCGFXf02kdtTgEOOZ8RHb2o8ap8GpfqFO3Akk3e16gMcKlMphpGs2LXVH6dOZ6PA/yX1m4lQVh6AZjZUdgoHX5twu0Uwomhy6XnimXO2thH3de2k7lee19OFGP1eRuFQC5WkYNzMm9wlHEm2wPlaguGyKGybJZmHQ+XnFtOvU3oO05MFODqBg32aCGEm4aC2K+tbwqEGAzjavlyTi7SAuNUaUg6EYqqP95iGIOBwGA61XtwPYrleOij6s7dtCLaGo3ovQrXVTTLgODI7KqyVWpfis7dpCEJzOArHro+g6sbbtCHYGzh2FcAOgaOJF6TSYd01rn3jbdIQBByGPIftQ1uOgePQhmDnmsNUnaNrOLryHMWPr2vDSsOGYPeeI2m88dWhcOx6k5q+Yc5rDk0/6NXsXdC0aQiWyLJePm8AR52b3QdH0+MNXMhW9IaeSmXHYrjMvPbX9bYNwdowYUN8yQcfD8VyH4z7YnDxev5mHB7iXCyCRZ6YqnEOxXgZBde3Mlxc+8Gj8v5tG4Kdu0URhtN9m33UwrfxHLAjdFxXN86LMoe3sOu8B+DoERzHZCSAA3A0EqXU4Uj7G/wl10FbXRBEt4DjxHBQ/z42C6FaiSAVjrT3mQAOaylnuZ6QXqe7M93NWFiAgTIcWbGqos6SpdvEjpgEHLbgqAGgKtwAjhPAQfVZ61oSeTpP85sWwGFLjFZoiy56Wb2HowgI9TQ2P8I635InoQl8HlM81hpwWDb1JZqqcchjrQP/+pHSBiLAQS7c0P2G1lk4dChchEN1RSkf7OI8HK6eOyqfGeVzwJGFkVx3uHFeB+Cwpi3kF2l8rW/CARyWax4wwAE4AMfhGQsMcMAABwxwwEjbP/W++mscw0RkAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Question 10.Choose the correct answer
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,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)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,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)
Question 11.Choose the correct answer
is equal to
A. ![](data:image/png;base64,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)
B. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAc8AAAA1CAYAAAAnBmDgAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAjSSURBVHja7Z09btw4GIZ1gBwgAax0OYCjcbntRAhygIwFVxukCgQEqQPZnYFFLpAuXVJsnSbtNrmBC9/Ad8iGGlNDa0iJkkiKUp7iARJ7fmR+38uX/EhRydXVVQIAAAD20AgAAACYJwAAAOYJAACAeQIAAGCeAAAAmOeestydbrfZxzRNbtLtuw80GAAAQId5XhbZqyRNb4RxJknyC/MEWKjIf+uXdgDyN+DMszFRzNN5MsA80PkAOl2WTjFPQJSYJ+aJTgHzBDozIN9oN6Bsi3kiSiDfgHYjDpgniQBAzo1rM9qN/MU8SQQg52gLzJP8xTz/zESQsajJzr/QnoB5xmmeaBXzxDwjSYSqzE/T7PxT8+8kuSMmgHnG12ZoFfOcbJ4icfKifLnEgJVF/jIvq9NYkqC8uPjr7fX1I/n/d9v0Q3KS/1B/BoB5olVisXDzFO/LtuWbJQftPEs/ZcXlqxiToI4LggTM00t7oVXy15l5Dqnb16WKNP+29GS5vn77KE/Tb65moC6TQIxmKQUti6rcPXuRPf2cJumN66oG5hmveaLVP8w8Za2+ffJDXxLUhnOS/HA5Y/NJXVJJstuLqnrie9ToKgmq6uJJ9vTF5xCDExFPMQNXc0Gs58Q0MKrbI0luzSeWmOPrr53Su7OifK2/xvQO8xymw6V21qG0umadhsjfw8BWab90831XlqfCC7OsqAbPPNdcojgMEMyilQGfOhhwmQBFllUhOhk5EBLx3JXVM5lk8mexxPjBzkYdnnc7qu0k26Qszl63B5vN6zDPwTpcqnmG0Oradeozf+WgQw42yvLysfydeKrY8zT5abo2P0FcwNZsYYpNw/SI9jxLvkxNQlcJIEbooWb1+2Q/7uhlZxdLdUEkv25jmuuy+9BZ0/7nD9uvziXMc5QOl9ZeobS6dp36zN+9Hs0V1S5P8zKCDBWsKWsJdYkjL6r9TKBbtKbkDC1IcR3q31tvyvLY1rrO3+Vs3EVcxbXsdvq4jF17H/r9dSlKI65mRqX8bo3mGUqHLr+3q62WptW5dDokBlN0ahuPofnQzIR7Jkam6wsSxAedTGv9dMpa0Fjx1In9e4p+KKN1i9bFvVpqAoxpi33bhl3LUzt/NXHU0nxMcXX1OYPMU2OQunKabD+TeYrXFvnZe3XN1LRmJb7zMFtL7/p2tcvc8xGrkDoMZZ5T+63QWp1Lp65i0PcZPszzkHPJr77BhXjtNtt+9Gqe+47BnCT7+vJ+mqx2KPsRQHYr6/U+AyeSZZNuvoprHGqeU8rR7QRw3Ra+yxpJ+vynuKa6w6sX0g/XF0Nch5aCnM88NaNXXX7pzLNrzbT9ue2BnLgf+cHGPl15Sck9H3kXSodzmOdStDqHTl3EwEanPszzMGgYXwVyFjxbAbQdP1Qnp5aJ5HdZm2dHB2kTYNPvXLaFX2HuF9S7dvDNHVdXJdvxI1hz2axv5mmq2MgZjHotugFq36BVN3BzmXehdOgqT9aq1dA6daFVG516Mc9mk1oE5mljMMeun91uNunXsTX5oYFrv36weWpeZ/Ow5a7gu2oLn4hEOzk5+U/OcIzlxJni6vozRq+dKKP3fRk2rdqzwbZ56madRwK//50pX6XJmtpbl38u8y6UDqd8r+1D0Zes1dA6daFVm/f7Nc/x5XT3dXfLXam2i7XtDsIGXTKo502Ony0fj1LUwI4xzzFtMSQxbdvMlHR1Qt6PDJvt7x3XGjquU0u2rr5flE/VdUiRa2INs/2+tnl2DTp1g7YhM9e+/BuTd3PpcOr3tnW6Nq361qkPrdrqVBcTJ3nocuZpezG65BtjnmKUNOXQ+SEjDbvG1ovX9v48kyhtBDm1LXwgBaYmn7puorvW0HF1XbJ1NfM1GcIQ89R9RnNrxyb/V3aUY5cUXOVdKB26jNMYncaq1bl0OjUGtjqde8NQVDNP2WjlZfl4yk3jTharJ848+wLdVyZy1RY+6NoZqrv3KZa4zv3+rlKqsWzbtWbaaudym72RHZ/gadZ9go22bOsw70Lp0LV56rQaot9ai06nxsD2vb5uVWkGchYbQYs8//toyc6ZeXasC7ZfJ3fZTa09hzfP/mtsi7JvDcVVW/jAZAA6UcYSVxcbOVyYr2g39Xi+ro5OtzFIbUO1/etZxsBd37rbL1zm3RLNc01anUunU2IwRKe+zFOdfXa9TwxWtUsBrgJoIwD5mvaFNiMA5XipmEQ7ZDNUO9h9u/dctYUPHmznvj8Z5LAR5tBmMcVVt6YWokMQbXBY9+y/17ldYpMiloZrmjU0txro1sIMf3f7VhXXebd284xdq3PpdEoMhujUl3nKtpN7FUQFR/37L8vycX2Ih+Ezg5QPdMKXF3S8BmJfQghunpYjflWUpsC7bgtvwrw/MFm9rnaSxRRXcS1Td0GOXTtJ0vTmLC/emw42aD9oob3jVL3VoD5YXvNZpgc22G6W8ZF3SzXPNWl1Dp1OicEQnfo0z2Z2+Xvgu0nT7w/02bpP1qt59u36WypjThiy2RYPMJSu5+SaOg9yEJ0uPUZRXpcPk1nK48iGdFhDBwWIErwM4jp2J1a73alupEwO2s8+AfOcxTyX9FSVoSWGMfd1IUhwSbOxqPXoJLneqntiBXmIVolNYPMUNfTDTd/7MxNN4jyepcWxW9TlgGBts2lYJqPWZjAGwDzDmGfXpgSbE+jXZDZLerg3AOYJ5O9M5tlsZ86LShrGg+OeLGaVU094iWrWGeFB7QCYJ5C/kZmnMD7dbr4hp+w0n5MV1ZKDZro5FoDOBwDztKbv0Uc6A7VZJ43SOMUGDGacQOcDQP5OMc+17qQFoPMBIH+9med+E9Hzn2vZRQtA5wNA/no3T3F0GOt/AHQ+AOSvpXm6OEMSAOh8AP4Y8+w6SxMA6HwAMM8Wa7jdBIDOB/ME8jeYeYoZp+55a+LAhCzL/+HEHQA6HwDMU6Eszl53PTOQ9U8AOh8AzLNlnCbTjOUBzQAAANHNPAEAAADzBAAAwDwBAADm4n9i37l5HQOrNAAAAABJRU5ErkJggg==)
C. ![](data:image/png;base64,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)
D. ![](data:image/png;base64,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)
Answer:⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
We know that,
⇒ ![](data:image/png;base64,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)
Therefore,
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfQAAAA4CAYAAAALiwrxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAnvSURBVHja7Z0/ctVIEId1AA4AVRYZBzCyw02NysUB/KxytBQRpSpq461nMldtcQEyMgg2JiHdhBsQcAPuwDKS572x3sxoJM1IM3pf8CXYgDTq7t/86enO3r17lwEAAEDaMAgAAAAIOgAAACDoBrZ1eVpW9WWKA1pX5WVZb08xLgAAOGpBv62Kl8VF/SrlQb0u8vdFdfsSAwMAgKMUdLEyz/Py8+u7u0cpD+rd3etHZZ5/ZqUOAABHJ+iNCJ5kX9eyshU7DdlJ+TX1yQkAACDoqxbANxf5X1lW/LjZbp/ofr7d3jwpsuwHW+8AAHA0gi5X51lx/TGFQWuOBrLsp03QBddF9pFVOgzxA5F/0dpW9ivL8p/nVX3F2ABAMoIuBTKF1axYeT/Ps29twLULerPr8Dsoc5YOzpNaZQJYV+dXws7yizd/MUYAkISgt9vXaQhfs4Iqq20TfHsEXU5UCMjg5gOH9hSrb4iJBt8NjlI0I7b9SEQy+2gSR3kW3a6IW4RAPvzzeQKeWHHnxfX73WrKUdB9HiWo4wDzEnLXp7FljZ2EsCEEPW0xgWX9H0G34CKO7dmiEP3fA6tsSbZb2sWPTb19Fvo5RdA9y88+iWd0FnQZqD2eo+NYKxR0i2jrtuIRdAQdEPQoBd1V9PYimv0SZ+1z3/UWW+3y/xos6D2/RyA9bmw+4GprCDrbvcA3WD6YydWJwwpEFcizs/zTXEl04hxTPQd3DbL73/N3JIBDrw+bnYTY5cEOERNA0BcXdEG7zf5w691FkF23VboJbM3zFdfvx6yafAt66K1fWI6dXStHSMJ+qjLfNn/OGTpCgv9j+2sU9JOTk//mus7jNhnQC3tsgr4XjfgEAtrGPvsrkflPMZGsyvO38piJoIaQ4P/YftyCPuCcWdZ6r2/rx763socwfIXu5/xziiGpOw1cp0uDWM/PEfT0xhz/R9CjClpqlvmDlf0CwW6pLPcphlTf3PyhPkOz80AVu6iRu0MxFlxC0NMac/wfQZ+N9kqaebUtBbQ7o9xth/82zDmuro0WdE/bWz4NieYxaYh5rKVfbbYoJttlVV+mOO7i2CPGAle+z8/xfwQ9cPAyC/ruDrpybn54tj3f9vvQwjI+trZ8O3Q3cx+WR9jV/hw97sqJJlsUQlFc1K9S/g7iimqMOQv4P4KehKCnVMt98CzYY0Kct/EWOwdPX3xgdh6PkMsaC1mefz8vq7eu32Zbb569KJ5+yLP8+5wTAJ09yhyX1O1q7hoX+D+C7l3Qddnccwlsat3W3Gf6/rqt+TSiqii2c+QdHHYPy36JxJyYAomutLDLDYb4nn3eFX3XHqUPpzIp72t/HNuWNP4fj//PJej7yboyfvnZl01dn4rJc1FUW+sKvfkl8XL5829zBzFZxjXW4Dl2kuIrwPkyIhHI5gi6aslSmd8gDDS2MqYPrvLoiHySGaJ40Rh7TOlM1iWhVgb6GCYoPrfb8f/p/h9a0OVESE6A6vr2sfxZXW9Od1dbdc+mna0sMOCpzfCdDMVzDXcfz6SemzXnnYHG23TcENvxSlPSV5PAFeO2q3UnaEFBT2mHbUj7Y587bDEIOv7vx/9DC7rMGTPlONj8LRpB331szuCCiLm+QE64HRFTouMcKx/XhB/xLJuN/hulZItLC3pKOTBD2h+PyYEJkWyG//v3/Sn+P+R7DLUH10qopueLStDlg+rOBlKivihe+TTYrgHF1FLWanD3HcRUW1J3LkK9h4+gmlIWsEnQ29Kx52/3Z3Bt9Tmdb4vvpVap68tUV23SdktlDe2Ph9hBaEFPwfeX9H9f42/7d0IJercBWd/vXhQXf0cv6NIYuMdqN6AYWsq6bh2JnAzxPE1AbZI69s8W4j2mOnVK2+0mQde1Xa2r8yvd7L8rXMKG1UScvnPE9v9fYfvjEb3o51ihp+D7S/m/j/Hv8/9Qgr6fyIyfkI0W9CkNT+DQQGxGYvrZ0i1l3Zy6Te6wZbj6fo+pTp3a0Y9O0E2rZum36vjoBLlPpKVNDi+DnGD744GNoIbYnq7ftktsSMH3l/B/H4Le5//BBH2XrLmAoIM/IXdx6v5Z3bwtZYc4h2imI1d8xi1fj+8x1alTK7rRFXTd6vwgaNz/zCRufWVnpU0OiRmptT8e0mdijO24+L8tLsTu+0v4/xzHbeEFfXxuA4KewCq9z4DGtJR1NcYpuzCNMd/PdHdXVizPGbo1rkuQGLo6iGGnqivoNj/WidSQFf6BoAdufzx1fEO2P/ZpezZBT9H35/B/377v6v+mbzL1eZJfobu+/JoY6tQus8G5W8q6IJ1TNVz1vEz3nL7eY8osfe7tdh/2M0TQdWK2u8p1Vv4rg29fHJgi6GtufzzW9kzf2EXQY/P9Jf1/juO2GJLivAs6Z+hhg7ur8cTSUrZPZA6MtpNo5PM9pjh1ijWujVvulmtD3fEXNzNkMBU8LeylQccIerrtj8MLus7/+xYBsfr+kv4/x3FbyGtrO111SMSsyvLPgyp2S67QoX+V3nd+HktLWZNhdmeaOof2/R5jnTq17HZb8NQlv6ljq36XZjU1sCjMwRn6Ctsfj+lHP5egx+z7S/r/lPF39f+Qgq6u0m1/z3Q1+mDGt1TpVzA7te3Dx9JSVhdwdlcw7q8gtvei863qqCHeY6xT685bY0e9s9vd3pSBQbZgNa2O1G6GB7trhvEYkuWefPvjgFnuNv9P1feX9P/Jx20O/h9S0OXYyZoQYqdMff/bun7cFEcy3ZE/GMAFmrPAcKeOraWs3kHa5gLqM3UNNMR7jHVq8Swp2fx+JaM/3lJrQstx1HVy0/07fXHg8B76CtsfG44nlhb0FHx/Kf+fMv6u/h9a0Her8Kq8PMvzLw/8u3OP37pChzhX6QAhsfUwNwUk10pxKTOmUhz+fxzxOdpn4wPFLeqMBQQXLUtW73azOdWtCFKt5T50orPERAVBR9ARdAwHYDC75LlOm0axLd2UMTaUYE6129oQluy2hu8TlxH03tXI5tm+AUVbYzjVmvGAffpi1Fmdrh96JBnWPlhbO2dA0FcWLM2JPzgtYJ/TgtraBFDtCoZ9AoIe4Wxb9EGWDvqgFOGKVhaAfS4V1FJramP9HgnWIwAE/WhWP7os3jGVoACwT3NQa96lqLYpfw9T0Q4ABD1y+tpEAmCfw4KaEPVUc1OaREAm94Cgp8das3MB+zzmoAaAoB8hbSISZW4B+0TQARD0pBFlMTkrA+wTQQdA0BMmxTaZgH0S1ACwfQRdwVa7GgD7RNABEPQEWMO1GsA+CWoA2P5RC7pY+ej63YoiHkVR/kNVKMA+EXQABD1y6ur8ytbzmfN0wD4RdAAEPYFgaQqULVSKA+wTABKfbDAIAAAACDoAAAAg6AAAAOCD/wFICcrkD9+78AAAAABJRU5ErkJggg==)
Integrate :
Answer:
We know that,
⇒
Therefore,
⇒
⇒
Question 2.
Integrate :
Answer:
⇒
Let 2= t
⇒
We know that,
⇒
Therefore,
⇒
⇒
⇒
⇒
Question 3.
Integrate :
Answer:
⇒
⇒
⇒
⇒ We know that,
⇒
Therefore,
⇒
⇒
Question 4.
Integrate :
Answer:
⇒
⇒
⇒
We know that,
Therefore,
⇒
Question 5.
Integrate :
Answer:
⇒
⇒
⇒
⇒
We know that,
⇒
⇒
Question 6.
Integrate :
Answer:
⇒
⇒
We know that,
⇒
⇒
Question 7.
Integrate :
Answer:
⇒
⇒
⇒
⇒
We know that,
⇒
Therefore,
⇒
⇒
Question 8.
Integrate :
Answer:
⇒
⇒
⇒
We know that,
⇒
Therefore,
⇒
⇒
Question 9.
Integrate :
Answer:
⇒
⇒
⇒
We know that,
⇒
Therefore,
⇒
Question 10.
Choose the correct answer is equal to
A.
B.
C.
D.
Answer:
We know that,
⇒
Therefore,
⇒
Question 11.
Choose the correct answer is equal to
A.
B.
C.
D.
Answer:
⇒
⇒
⇒
We know that,
⇒
Therefore,
⇒
Exercise 7.8
Question 1.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:f(x) is continuous in [a,b]
![](data:image/png;base64,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)
here h=b-a/n
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![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAA+CAMAAABUfxaqAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjoAOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZmY6ZpDbZrbbZrb/kDoAkGY6kLbbkNv/tmYAtmY6tpA6ttv/tv/btv//25A627Zm27aQ29u22/+22////7Zm/9uQ/9u2//+2///bZ2LdVgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABT0lEQVRYR+2W2VLDMAxFrRQatoa1LZilSqFO4///QOSExUzjSGXEQxn7KTO5OZGuZMvGHOJ6vQI45wOXyNrLe1MXDxxsRIYwWX1/3pywrCBOyTBm4YwLq3ufksWsWmAXoZKyiIUyVFqGk5clFLf0O0coN08l6evTvswjMizOng3C3LQV0Eqx/GK68ZbKPCbD0AZtNZWY3pTJsPuadHW0x5sfMBti7Fbccb9j7Ubp19dl2oJePxzXDiv4Zdi4er+4JnVBxrKACvTE7sOmnJntDef9xRLgiN+Gj9Rdb1WyZyRtkDX/3oHhPauU9td5sOeD0u8/MX+ao3KsB4Xza7qpCI4iSVIW7sy2iu8Hkq+GNTYMuTA2tZZTZFmdHENq3NjZI32/4AadGEbTVazlhJYGtdLCcFtxKll211tvVVgfh5MKS8mpjMkOZAeyA9kBqQPvQQcTtq5GphMAAAAASUVORK5CYII=)
Question 2.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:f(x) is continuous in [0,5]
![](data:image/png;base64,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)
here h=5/n
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Question 3.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:f(x) is continuous in [2,3]
![](data:image/png;base64,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)
here h=1/n
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Question 4.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:f(x) is continuous in [1,4]
![](data:image/png;base64,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)
here h=3/n
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![](data:image/png;base64,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)
Question 5.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:f(x) is continuous in [-1,1]
![](data:image/png;base64,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)
here h=2/n
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Which is g.p with common ratio e1/n.
Whose sum is ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=-1
![](data:image/png;base64,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)
As h=2/n
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=e-e-1
Question 6.Evaluate using limit of sums ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
F(x)=h(x)+g(x)
Solving for h(x)
. h(x) is continuous in [0,4]
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXgAAABPCAMAAADWSy41AAAAAXNSR0IArs4c6QAAAL1QTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmY6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZjqQZmYAZmY6ZmZmZpC2ZpDbZrbbZrb/kDoAkDo6kDpmkGYAkGY6kJBmkLbbkNvbkNv/tmYAtmY6tpA6tpBmttv/tv+2tv/btv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bf/m2FgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAHgUlEQVR4Xu2ciXrbNgyAJeVSt6Td0nhpdzru1nWWl2xVki1SrPd/rAI8wUMyLVuK7VJf46+OKAD8CYIkSCVJ4hUJRAI7R6BZnO2cTV+DQfffXUfwwzd0lZ7c5tmNoaiM4IcHn5TZp6Q4eaKaIvgRuCclQIef5SRlF/r+wYMv0x3o0wL81+XxxU6Cb4pTI/KM0e9G1rED4Os8PYOfK13zEiMO+T4yk1HUFaeL1JpRjKL3UJSU6dHnXnUpju6SsuezvRQe2kPrwmsWvDNjqKlfzQ8Nx3j1WRd8cZXAvwh+4xZaE3z9jYhMsHBp/n7ZUFPx6bt5meupjfEMJ6A8+vdjmv3WpqB5+DZNL/VdtVAsztP0+GUjTTOzpzBNke4P+Ox7GCXZqs9zNbOzp6bIFOBmtkuTNViyatOY9cvJHoEHqstJ13KozlWz1PkugU8g2FjRzkrdDBcpNpbMY7y0t1ABk7gSAV+1dY2N7egnAFZMpstU++PxBnin+s3ju5ynn9jVGpP6cdv4KTfMbyxyLAGmx9taMcYnxONLK6aOZWWrHjfMv7hJgQYwlMtJS+iu8C4BT8bZQPlDF4MwvzfRxWAB+V2YkLc5Mg6mzz+rwbWZvezM3deKTpgfuqm3JL98+7FrQg4Jgsv/JzLIrwbf3L7WuZ8SZqqDXxjmWybDqNswKMyYUcwOM0WWWk5cjy/pXLqZvaX58PpcI4GY0MFHj96do4ihTDzTEuYbcKirxDKoo7pENDXbesJngEdoYLFg+t71CRsH+OWsr2gaLWwqyqS1FyXKlNXeMA/TgqS8WmfBR0R3ZP98Bnj4BRYLJb8KfOV0CNydExcZozv09QAPk1x3I5Jrcw0SDuLpfJQVMduyNZBoYLFQ8HXumUFoHehl1kV8Zw3w7fZ4K+QL86zTeAwKA9/u8oFEA4ttCP4vkaMXaGH5e/IEXoheJfp6fZ2mb8AH6S2/UrSYDQf4cZ9Dgo59yKvKpDL6OIR5q69VsOxLb2Rb26m+ZkY8nivK5lS0DlHYqOBOuNyBbcaTJ1IKKoXZRfl8Ir4zw/x2hnJ2ylW+swVVenHHE2mymfGLrBvbm63zadL8gS1Bb3nN0CuHOr+YQxS5+ATnZ9QoopUZT0Plrc7GPF4YZKf6lHFcBiiaPr6aG6L1lnIzg14O+FEc/E+Xwko9YkATz6vvDLyC0hs2fbAFPNpE6glmgseLJRnLArEP0fn1LfR/cRGyasnG3JVl5exkkWfsXdh73IZBHK/2csPjuQ5ZBTH1Isk2bPblezwbiHXicpkPsQbBjTj+vPruCIN7vhzYGk3iB69QqU2VOn8jowOawxfGvObk1kqPZ+DlBy9tL6WFjDq3RxfGhu7ySPAuA3HHEE3A4+3qCobb5oPs1fgrXiksx5/X3zvs1FX2beL4fieq7Q01CrweUXRwsMHTuOEjT0NNMHgWDszL7IJmqs8JNawvtIFHr17ACDCv0ZlUKXF+jcV+Dp5xE2NNi4Os4eRG0dJ3aEXrUOCX73+Sgx0GS+rx5FZYqAnxeE8KyY7xnaHGA570oPLonx/hnOBNySao0s10fot6vMRlgd801KwAryYRH+Zya4WZx2d1PMbrW/7W7+PxvmQ10+YLIqjWjvEOeCNrWGV/QiWK098xGaLs01NVrsWcuo7i8Wq4EbobPIZQ8c7BJ8R4rPf5HZSjt1rAK2kCHRtcVfJUj236ce+2GJ3HW6k+G7wYq6loZrZEuZygl4vTorpUlcJU7Z7NJ3nDye/8ixyD+0YXK9S4Kz6YyUH447slbKEIU68MPJ5vRPMlIBzGyS7/y9MpveW1SEtjIvWHHGS0Mvm8fznNTw+LlauZ6rPAow7mKUQ0M1v5MBtpxVKYlIIFRvYrjq1iz11859xdOzdpgWJFnqszV7OJ4q5ni45U9Tq5GqKD91MI60PZvK7clfsgHdnJdXWFlu/ejQzPTlLuPKm6mIbaMHi5leDN9PcYiW0xlrRW/SDy8av3QQZveltB98GU0c3prVBlprwSPOuU3pq286DjCmEp0O0o36oUkZnyjyqDu5f1Ht89G+Ku0+PPkPg79m0jOqcetpyO3SrbTmE6M+Up1noYYWv2We/x4fAGP8+/YCLwtfuSjRvgd+78SSgaBr4N8PD9WLxOps4BZ/MG14v4Lh/7j3m5qbE6371jEGHoO8G3bKSFSQ4qZb3HJzz+4fzizuPxuEfhXAcJvn0nMohqQCETPIvxzxDe5/jhxHideSL4DxE8Ty09s2MTw1zue3wderwOv6fHykRyx5d1Wv4wZydxl5NpstjPQ3PDOMt2pLKklExwGSLhlwr3/pyF3g6V3ZDyAO/gRI8fvy1whVIe93s3dmhr4dRe+9tcQysfWv5ylh7f7sJfkPBUtDx7iq/eDu0AIJ8lGMhfTcH8ec8E/AjWHpIKyA/UJJEAEy/+4nO8BiZgLegi+IF5K/EcvPoDTTHUjAtea4NN6Ti4jgAfEwzmIg+O705HUBxVRAKRQCQQCUQCkUAkEAlEApFAJBAJRAKRQCQQCUQCkUAkEAlEApFAJBAJRAKRQCQQCewHgS/nNQTyfJI5sgAAAABJRU5ErkJggg==)
here h=4/n
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAA+CAMAAADOHANyAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6Ojo6OjpmOjqQOma2OpDbZgAAZgA6ZjoAZmZmZrbbZrb/kDoAkDpmkLbbkNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bBV8yOAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACVUlEQVRoQ+2Y23LCIBCGwapptcZjDa2mWonJ+79hl03MgUCEODlcwEwYJ+OyH/8urCshbvSvwN+G0s/+3So9xusjuUyCkdAARvTeB0wobTm5QkymNc/hSiuMxqKFkJEnwTC6I3f/7Vxd69KQMmqLFiyxv5Vh5rBMSPeVxcKm9GUqixYshK24KjM5wHBK978eniIOE6/iyc4kizYsfHlTwjARpshbBKhR7FMYzTBVizYs8TogKpjIE55xjjx95pZc2lvIvMkBHAFMKG0a32cwsS/BMKESjlJ8Gy3MZIKsSEcVJjmIjNTBqJa2t9AA1sPE5jdLGHsLU5hwBiwcgoN5UAuTYhl7C13k5BsY7/2EiWwS4TNIYHsLHQvkTfWiyRJ0BRiQTOJUPztO9hZmKd3xt0Jp4x27e7I8nhYM/wjG+GBGIAoiCGVEAS6qcFaKhwDEMGU1D6vw4kjku6UjrnoZK8M8LrG0xg4wajBIhDB5/aUFV/HulU/aK7YUpgdHT8oYhKlQpv84NYRpABhx+eINXFRhVSmO/fQnVZcDqzIWYGmSnfYB0+VG3dq9KFDqGQ392VsYLgxfy3tGYxN7C05nP94kLz+/4v+NeEOn5wimU8mxTc+YmtlbQFU+EiY6jnR87/C5b70duS7z1xbNSL4B4/al2LJoZODJO8ZJkHxBJx/CtYYfHsN+aXsLAYJPVZnLx+I0nDIZC+bMHdIlEFMtZ0x6xpe0pHO4/J81X+Y9YxFY0y7T+HiWtmnYM75gYU/lLJwCTgGngFPAKeAUcAo4BZwChgr8A9g3NEH0enSpAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
=8
Now solving for g(x)
g(x) is continuous in [0,4]
![](data:image/png;base64,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)
here h=4/n
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVIAAAArCAMAAAAdUfBgAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6Ojo6OjpmOjqQOma2OpC2OpDbZgAAZgA6ZjoAZmZmZpC2ZpDbZrbbZrb/kDoAkDpmkGYAkGY6kGZmkLbbkLb/kNv/tmYAtmY6tpBmttv/tv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bdFLsJwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAEJUlEQVRoQ+2ajVfaMBDAm6qzm26gbsI+HKBGN1vb//+/290lV9KQNCll8pDkPXiI13D55S730WZZGonAuyYg88W7Xt/bL64qEtJdUW9+PcBU9fQGkVafdzXtMc+zmuDql5OSrFT9lcYYAvIcry4vXxTSZj4bM1u6Fjz9I4KsrxaZQpqVJ4+JyygCSzTSZg7uDkglWCh9TmN7AspIS6EHOn0y0+1x4pXy7IUn0I4PsT+Z6QioJj5Gmi3XmEdMfayXthjRYDnVN7/cAowUlEPEjoHisdOOldtaLbkO73CeaqZV4fP85qfIvwWVpYgXHn+vhcDCIlI8POFuJbZUq5m7fLyZ+5jI8xcVz3qHynRDo766y55xE+PEQ9Pt/P9+tSTbnus366lz9cZh2txfrtPUejqLybHkh5XIf8eskfYnXjxmyrEypTi7L3LIfHrUopOxFM6ayOPiy/Y4aOZf2oxAFQQRfipPHpofUZYq8YSJFx+LK+p6md9RgO5Rqw+ph3QbqKy030bqKV7RZUy38da4z9SjscTftCJ2/BimlfSyVmHsR1/8DiG1sn7b8UcilarrdZhIIZrPsESaPRUQZOlNrcbdImXSbZyqrlWkB4cww5OFlKVWsL/44uERK0GJEs4jS3xfVsras5Xaq7CttCpA96q4WGRSXNy1KANI6SoYVXGb/cHPNaC99bFiKdi6Cb48SFmsnmIRTDvdEd8TUlarKsQ5vEgltYolV+ttoCfH10iJK0gxqwBSPjPwtHZlVt3V+6SsfqFXTG/BnpCG1DJD2wZS4qrMj5G2+yDoa3Z8jVRVrVaZurF3TqnNLXaLaYU3DUJiPlMVX7BDdrrbrmPnx3rVsjOFGKTWNYxU11bKRcVmH7VjUF6prpX6xZxW+h+R4u+1K+hRK8LxHVbqQdqxUnurTIXwf/4GlkU+0Ofaj+MPar/1WWkgidJIvQVqZ/X+MjZSbK9nqV97hykRtvWbDk/KVAJI+cgtxW3WPG32S7oG5ZOywpNXLBJpM4cTSMKiuPSzvwgKGGX4egUhtcwcChtMkBWImfWmsiOnF3JB2m4dZLL5V6Myda/eI2XfIfSJ7RcpZuuuNTqMtPerUNsk3TMZShTsp7+5l27tDUYK7RZHrmccB91O1PD5j/AKvnfP5b8KWkbl3+mXHiGg4UvmdEyX/6qmSrfzXCDb3rT65xM9UXItTh+h33KKT5Xx0DeddQ+A4v+grHf4Lh7sFdyb1gtYQf8IXq832FO6NNIh3asjpJplCvPuXdddv/YxknzRfIdIhO1e+tAOdSPQQJqivMePuJHatdLnTxcPXSvVj5kZSJORRiGls/QVjtEFvplnqb5LtEb6pl2LQzpXuTcdozM+pEvFPuWj6ZHdGGYBGXiwnMp/bBlO0oPlOyCapkgEEoEDJ/APCj170d/sIx0AAAAASUVORK5CYII=)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUgAAAAYCAMAAACvM5RCAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGaQAGa2OgAAOgA6OjoAOjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kLbbkLb/kNv/tmYAtmY6tpBmttvbttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2//+2///bX4+QqgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACzklEQVRYR+2YbVPbMAzH7bCu3soKhbG2sI52A1O2OA/f/8tNUmKIEz+1aS+8iO6Suyb/WNLPsmVgbLSRwEiACEg+PYTEgfJDhu6jPW9Y5U+e/AiGt40D+e+W8zkMFikPuj2x4KxhyWmafXkMRSyjQBY3G7ZPYLA4ecjpyd8fHRZUG7/2h1MsVqxcB0RA5vOOJ79iMqNZiZfHDNlXo/jkt0hWx4dVrqdMhkDeQN7hkpcXT+VDVFWSw3h5X0hR38tkw7aT9OiwMgGzELCiDbJc2z7CRWEsDLuMsT1ukSRtyl3qUHRHve86kwgRr3YWkeMrHgGyvbT7gZTE8cODzO85T+ap4rChZwIwKc5XLwIaJd1qy6B1Xj4xpgSH1y7ooKJuDSVvNBsTpFbtYC7xejO7TEEQCly25QNVpI5eV6QOq1xP0vIBSxQ7I9VbJmaPcMqbbapnaJlYsnx98VwrHCBR9YpLvwCgSxchrYIJu8bLAVLLigVMXTW/pnwYkDosqLkpXBQSZVEsIJPsMmWqAZJo4nO9IVLnoF/vS3uLCZJp3Lj3YjPqmJGzUwXfNmrdLauHHwakO6wdn/3B0DogiWaVGdGu7p49slKhp6a1edtVLFJWj9yZRIknkUxcMZiNT7BwTmlNZ47oyd3+K0fXYZBUbF6QVJ+4AbSsWTzVUrWpjIr0yGwVeU6Q6E9n4A/rVSCh9tIOVWSnKqrZspkJ0qVqgXTKbCBPWYG+DNw54vZIy9EHEjtSZ4+01J3rdN0Ead1Eq7EiZUOCdEdP/fgWCGRinubfsWvXrRsqgjoOmoK2lBNN3zlS8SUrXyz/rTD6glNlNhu3LBJkiacMCQnVWbR/gzu/oFi8F8ZbBs6w8ns4GX7D/gB/+N79hYMkNPXmrQp7Dw/nxNFzjMSTZ3Jn9ppOqTGnygTplg0KMhjWuTeZcfyRwEhgJDASGAmMBHoS+A85d1zhiiP4GwAAAABJRU5ErkJggg==)
Which is g.p with common ratio e1/n
Whose sum is ![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
As h=4/n
![](data:image/png;base64,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)
=(e8-1)
Now for f(x)=h(x)+g(x)
=8+ e8-1
Evaluate using limit of sums
Answer:
f(x) is continuous in [a,b]
here h=b-a/n
Question 2.
Evaluate using limit of sums
Answer:
f(x) is continuous in [0,5]
here h=5/n
Question 3.
Evaluate using limit of sums
Answer:
f(x) is continuous in [2,3]
here h=1/n
Question 4.
Evaluate using limit of sums
Answer:
f(x) is continuous in [1,4]
here h=3/n
Question 5.
Evaluate using limit of sums
Answer:
f(x) is continuous in [-1,1]
here h=2/n
Which is g.p with common ratio e1/n.
Whose sum is
=-1
As h=2/n
=e-e-1
Question 6.
Evaluate using limit of sums
Answer:
F(x)=h(x)+g(x)
Solving for h(x)
. h(x) is continuous in [0,4]
here h=4/n
=8
Now solving for g(x)
g(x) is continuous in [0,4]
here h=4/n
Which is g.p with common ratio e1/n
Whose sum is
As h=4/n
=(e8-1)
Now for f(x)=h(x)+g(x)
=8+ e8-1
Exercise 7.9
Question 1.Evaluate ![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒ I = 2
∴ ![](data:image/png;base64,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)
Question 2.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
[
]
![](data:image/png;base64,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)
⇒ I = log |3| - log |2|
⇒ I = log 3/2
![](data:image/png;base64,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)
Question 3.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANMAAABACAYAAACA9UI0AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAYFSURBVHja7Z1NbhQ7EMd9AA4A0jgrOADjyRUmrYg1gmllRcQiQi0hDjDJLhLKBbJjByd4i8f2bXKDLHKD3OGR6o673U37sz1tT/Jf/CSYD8bl9t+uKpcNu7i4YACA6aATAICYAICYAHgeYrq8/PyiWLDfjLH/GRN3J9vtK3QUAAFiqtbitKi2b+nPG8F+sEXx+/Pl5Qt0FgAT3LxtVbzlbHmD1QmAqWLanrxasuW/EBMAEVYmsa5O0VEATBRTWRSfEC8BMFFMX9b8myjP36GTAJggJhISX3/5JuOm9bp6j84CwFNMdTq83mOS8HuZKgcABMZMAACICQCICYAnK6aqPPzAGbun+EkmJQAAnmI6L8U7n2TEtvr4piirY3QsmJuqLI4/Vts32YppI/gViYeKX2l1OhBH17pNXEqhC1F8xyYvSEF92kGI7ylL37RvNHV5/MYlLU6GHB2I67kNof2wfU/f48hLPOrCbF78SjWhmxvG+K3LIFU3eefsOFk3WItKbH7spXuCIy9RoT5MVbljjZdsDfNZwXYFtfUpJEdw5GW/+3CymOrPJZxNazepKD89iYGAIy/R3GbX1YkSF0vObmJMxlYxmX6k9fc9Xawm1pkeHzSz0Lxp+zrRwtjdLkquUh15oedYFodfOWe3tT0ZuczUNkqEyedMfX1YVh9srp7LBN/F3HHGj/WHTD8iB7NPQzoBxAu267bOtDqqD6Al0uBLceSl3Ufkyxva1sgpXmsna+XZUntt47J5Rm4TnMuiEU1MpoHi6gr23JiHJTV25qpeLQ70afuoq9KOfifFkReXCTMlOg/GJhafcZmNmJoKc3cXp16ui3LbpILjiWmuBISsqOd89U/MzempR15CsqkxB9Eu2tm60yPjr/VuNGPT9n46MWncp25/xE0U9YAXm6ux743FIWRc//W+aHvu1gw+vhqftfB+1ijEjhhHXnzF1LbH4BqH2BJVTAZBjLl/rvZRlU7rHdHzOxGnqpim2B0spu4ft4uJPrviq5/0OZ0Im0DzcWApv9nMHOIudamI5Ozs7HUdrLfCSm+Hr5jksz0syq9H4uBanRzU9sW2JWhlGhl/tolc9135OnlH9LoqLLVdoXZbXZoYYpJlSbaOUKsByN+t/875rxyrG3qVC4PZc247fAZp1zZ+T2LqAvviuJkg+rNuTFtC2zn8LdvKqhubY1k+XdwYYne4mOQybMmiDTvQeVZ5eH+14j9zvofCNKHMaUesGV8XJ8eyxXcF7Qqtu9WgSePzrcm9HxOiLvNsipl87d6pmOrPPMRJvrFW24kR092jKW0N/i7TuA+d2o6xh2+KRUyTg68tU9t50abum01VGavQeCI32/S9MTHpRGNLQPjYvVMxuXXo+INbLBb/7cMZKlP5ylx2xMqSmSa6GLbEqOF0mYxji8nV7p27eb6dISt/q/Pqpc5nzgldOdWcdoTFIoaYdRi4R7IlhpjkBG1azUxiGk4iRjfP0+5ZsnmuD1PN+vXT0fkeTVCTK6nsCI1FhgNStlN9PaYtU8XUZiEt5URjY1M3XnUiC7F7tn0m2/fk68POVtuRMj1OoqHDkWogTK8NH2wKO0IGabvh/rj53KaJlUEV25aQdlIburjJbUXUJVmGY5ps7m0NPL4earddTNaMSRwxqZuX0oi/Y650Lp96FwahCmvUPZ7RjtAZX56glm0aFtnGtiXMHaX9L36rpvGnZCxVm+kZNrV+/W2CULuDxdSb3XBJJcguKeRWThSTSWLyLXQFYLakUIJxaW2QSUxteQauAAMZ4XMEIxsxhR4OBGC3yaI0d2lY/U7bqpP62DoAYxN8itBjsphyuFAFgP64zexCFRkPOZ9WhKsHMomXUsXw5uXSsdQ+56MS4BmtSjNdX+AkJtrRrzeqxOaK6pF8bmnF9cggeayUy/XIuuO6fv4qLu4Hacju4v6u1OLv0hIAQGDMBACAmACAmAB4kmKikgzU3AEwUUy5X5sLwF6tTCl3kgGAmACAmCAmACAmACAmACAmAICrmGL/X58APOuVCQAAMQEAMQEAMQEA2B/KNnpuqwImbwAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAABACAYAAAAan8KAAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAbLSURBVHja7Z09btw4FMd5gGy/CYauNgfIaHyDxVgwsu0iHsFVjBRGICBI4WIL2Z2BwBdw5y45QYqkTeMbBEhOEN8h60eZkmYsfmkoUSP+ix+QeDwePn78+d7jo4ZdXFwwAEC8oBMAgAigEwCACAAAIAJT4PLyzZN0xr4yxn4zlvw8LoqnGGQAIhKBfJmcpHnxgv69StgNm6Vf31xePsFAAxBhOFDk6QvO5rfwBgCIVQSK46dzNv8CEQAgYk8gWeYnGGQAIhWBLE1fIx8AQKQi8HbJ3yfZ+UsMMAARigAJAF++fS/zAstl/i8GGoBIREAcC4oaAQm/k0eGAIDIcgIAAIgAAAAiAACIWgTybP8VZ+yO8gMyWQgAiEQEzrPkpUuSsMiPnqdZfohJAYbdqNLDo7x4DhHogVXCr2jR06Ui8gb2koNrVfEQHSUmSfoBxUVgaMTN1yT5ELK8fZIdW94b4Lc2x4M0CAd7yfWQg0C1DLt+hIlr2x7nK1124+mnUJvQdDuV8e82C6xZXDRU2+SdBiEGyepmJ91YXNv27Lmym1BVrpPOB5g61cVj6KudU0hY4tr2bvdh1CIgfi/QDibc6TR7PZ3wC9e2fYRXLt4AJRXnnN1uu5EMHAPX9On6SBHQdU4V0zq446Ud28e/peoPe3Qpkp+M/eyjrDrUtW0awyzdf8c5+y7sGVFoRW2j5LQcZ+rr/Sx/ZQoJbDel5praCRGoJgpNQt6/yyM7SNc5ciHadmC9cP0lwUQ7B/JE2oTY16IJcW27qgG5n090tDumfES1wTTGltprmpPlGNkLs81mNy4RkDvRAJO+mvCaSW4bMlTu7r3b5TsTLvpkT3106bXve/qcENe2bUQ+JCqP0bTIXebkaESgbITdohibCJQ3Du1UV7h1aVaUR2L+RGCoxKC8Xcn54rPPgigf17ZdT2d8Tfy+2lnN85a5V3mTinlpen20noBwyyzOOIOIgOKz6jNu84IWCzVZXane0xZr06Cs/7wWmzW3fIAYtpl/qNgIyVxtaArLtvkFFxGwnUNd7PEmApqF3BYmuNhHVa2VR0pjeJycbNj2Q2HzD53N+sniwn2jdOWPYxKBejLoRYB+b8EXH+l3dMJRJoEeFkXjM6WnFLoslDg9Pf1LJNGqMV63I5QNLiIgx3U/zd4dJHvXurnn2x5nT6Bl7pk2H9175WvkkdJrTUGQ7epqs7fBFDumpkDHRgRak1cKdAPS1hFdRECWHtsMYLOCjmI68X/OP42tInCt0m9jtwphg+3iqtvG70gE6oRbelgK2+Ndzqc9Xdq5+TnGnV4zL9tODtpyI6WN7Iuw+aj4x8ZmrwNaxSgPahXKEzCKgPR6DIL0qHMNIURzEBcL/nGszznUTbahbfCxw+pyQL7scfFY6str9e5bHmfyQhcGqgREdZKlygnUIYCdzb254psfvEsiIF5PVldd8gjVBPBkpy/vqP3vtseIvm3oYsuj+aOJtU2enas927SzzpWVhTwyFqf5ROGY7j0qEVAtdl1i0MVm754AhQRNd20XRcBuEqgn3Gw2+zb2ZxjoylSHtMFH1t0k0D7s2faOic0m4lsEbG32KgD0oTuRE7AIB7oMorwNlp/nf6riwrGgKpke2gb3WLs9MavKuvuyZ1sRUHnILiKwKYDKcKDF5r9P/5sbRcDH6YAp075rpwOumV15krDen+O8ZttMeoa0oUusrQoV2kJQX/ZsIwLVqYahbFg1L5sx/vHZ2TOdOChs/rX5Xq+egHWdQICyYR91Ai470eYkabYj1DEhLXZ6oEozQUU/25yQoWxwXVxVkddD0VN1VKY46fBlj2s76fPrvICd92GV/KTXzs7+ILvXjknvfy53flebt88B8MVn00Ia+gKRqWLQtwg0C2fkADy2OUxo0HzOItEUhDHY0GWHlU+Lkm1qu7zk2x73sIW84/b8WFdvuWk3jWN5H6E+Mu1q8yiTVn2LwNqOgi8nAaNK1tqXDfsiWhFwvawBQN+EmpOT7kydCFRlmHgUORjV5jW8dxqtCHR5qAgAfRLqWY2Tjq1Mu3zIx4sB0LYphQhPoxaB0A8aBWB9zuJBo/469CHet1FV4Q0gJAAjyAeEyk9N17WyvDI61iu/ICIvYKDHzE1eBKgKThRJJKsrqpxy+VYhfA0ZCLph4WvI/Ln/Xa/VljEZvpAUDA++kNRnZ1Ylle1lpACAiHICAACIAAAAIgAAiFYEqPwSdwIAiFQExv4VVQBABAYSAogAABABiAAAEAEMMAAQAQAARAAAABEAAMQiAs1HLEMIAIjUEwAAQAQAABABAABEAABg5H8E1qs5SgHb8wAAAABJRU5ErkJggg==)
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)
Question 4.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
[∫sinx dx=-cosx]
⇒ I = - (cos 2×π/4 – cos 0)/2
⇒ I = - (cos π/2 – cos 0)/2 = - (0 – 1)/2
⇒ I = 1/2
∴
= 1/2
Question 5.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
[
]
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPQAAAA7CAMAAAB7T1etAAAAAXNSR0ICQMB9xQAAAQ5QTFRFgYGBAAAAiIhmZoiId3dmZnd3f39dXX9/f39dXX9/XXd3f39MTH9/f25ZWW5/f25Ibm5ZSG5/RGp7bm5EXW5df243N25/bltISFtuRllsgFszM1uAM1l/f18oKF9/bls1NVtuNVlsW0hISEhbM0ZuW0g1NUhbbEYdHUZsRkYzRjNGWzMzHUhbMzNbSDQ0SDMzMzNIWjMdHTNaRzMeHjNHWzMAWjMAADNaSR0dSB0dHR1IHR00SB0AMgAySBwAABxIHBwcMx0AMwAdHQAzMh0AAB0yMgAdHQAyHR0AAB0dHQAdKQYGKQYGMwAABgYpAAAzMwAAAAAzHQALCwAdHQAAAAAdHQAAAAAdAAAAAAAAesJGQwAAAFl0Uk5TAAEMDA0NFxcZGRohISUlMTExMj09Pz9KSktMTE1RUVhYWWNjZHFxc3N9fX9/f4qLi42NmpqgoaGoqam3u7u8vMXJycnKysrK2dnZ29zc3Nzd3ePk6+vs7P4Ak7brAAAEMklEQVR42u1bfVvSUBTf7sJGRTe0Ui/WLK2twsqhQwxnFpRaFhbC7vf/Ij175Q62se2e+bAnzj8KyG/nt/N+dhWEpSxlKUuJkPUdaaH1Qy83wCH3txfeLIpeAebcKIEzEl3k+v6jN+ca83JfK0UIqlxqkotzygCQY6kUpNERn0MShjTq1EuSbfFxBYo0aZemxhw2gEgjkz+L1XrUletqsbnstAJDGn/nVhSZ1u2Qlr/UYUgDeDdpSlgXkKkttn8zpA2QGk3aIHGS4jIQpIFyN9EEeVA8acxTXSek5ROQMFQ1Qf5WfOnj0haatO3aJSKNQdoxMq4L8kC7867Y7M0XjIS2IUnj0XVVQCalRfc5HKTxyK6pWjzp/XE2bPnKBiPD/sN5f5kVORtp1eaVIp1Gk76pR3Zdfe5JPgLZAd6MW270rP5qekvjQT9NgD37dTeDd1D4qoRHTju3FR2GNxvC+nDy2crP58kuNziV4EgjsykJNRO+z3SBu9HA8sAOG/X6XiJpMvkuLGm862o4hi5LicCq8y4eBe3jyo8oSytBiKYkzcQ0aln9x3t2lLUu6wJ6dd5Y71E9BGK4N1XR3S98SHkLIpDPwsgBsMgAI9OhIA/a0zHtBVsgfgbNTtrQBGS07WxAx3XBoPRgQ1BDUYzMtvdTZ17NlwD5ykY+nEUOgLs2a/+VR8HjnpTIyGU9TFqd3BAtibTTO8t7gbM5WjGuxY6hNmuXeaqKNhcZf/WBu7oYAONR271YELSx2ZvQppTH0sgc+xXJYFRjrTnZmiLzIDVnG3lTTERmgLsT4AykPcfJ7t4KpRfbSaqx68hEeNUKO5di0YsXCcgh4KtgPeIFM3OpeEtfvk6yNBv/U81JreU1ktGqkV3WeAcd3yDWFGTUPqllJSDPAIv+73GJbIbz55wx7XVHjTjV8B6rmi6gjp6hNNXOYpFngI981m6FxqPG3OxdzZm90VvJv0CUau4DhtpHKXv2TkaOAO56H+Gh25xUky09qdMp21A2kemS6FxAHthaGbZjEOrdOmXExmi2Oo1MvSKqv13krQlyJRb4vQes3qyKyrCR3HuTT9XcAwfaWetZdpXHQ4vSpr3h1OyM5LBWvMDN1ZGhnbWzOOQ5wMrQYkc3oOVW2oFjMWTewLEkvSQd2gcAkYZZMRRIOrQPgCFd2IoBinR4HwBCurAVAxjp8NgOQrqwFQN0IvPG9id/H4CpZBRu6ft/nvJ5pDeon4Apmn6pkFs4tfX3AYCHLwCedOdaWGdYQPuZ1gBLubdwMEvl8iUV8qH87CagKOGyEDO2Y6ADVewmoLCQ5nkwGh7bQbyShSxMyGl+AxFnanXHdiD/ZjcBC+ndobEdJn9PQS5e7lbo1NjOf0ySa8WQvg/oQJaHshyI1UFvYSmOPis6bMIoxyF38CT5H/47w1KWsojyD6IXBB8hKKKKAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
⇒ I = � × (0 – 0) = 0
∴
= 0
Question 6.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
⇒ I =
= e5 – e4[
]
⇒ I = e4 (e – 1)
∴
= e4 (e – 1)
Question 7.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I =
[
]
⇒ I =
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANsAAAA9CAYAAAAknhzfAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAdwSURBVHja7V0/bxQ5FHeaVFCjoDgdJyiz3pR0aJnLcQUFEptRRJEoBYpGQhRboNOQLk0+wFEdHRTXHgWUd8XlG6ALn2DzGTaX5xnPOhPbM7vrmbE9r3gSbHZnbP/88/vj52dycnJCUFBQmhccBBQUJBsKCpKttiRxtBtF8cHR6emdTjtJyFoQYAXSj1Dk9PToThxFB1Gc7HZGNmjEHqNnO3Hy0pFJehUI2YLoR2iSxDsvKds7O5pM7rZKNkE0Fr9/hpMU+9EXeR+zZ0A4k/Vh/aVANDo6fouTFPvRNzke0bemuW+f3TT63LWPhmRD6cqH+5nSTzqrzuqLIko/R0m6jZMU+9FXSZNoW6dwrGo1wvY+4iTFfvRdYkb+UGk3e1ptk3xzKSiCZEPpSrji2Yy+lbWbPdVJBuf7abqBk3Shdq2ZBMnmqSmZ7m8MCD0vu1TBm5AuTtI0GT8YUHIO7dIL+1FevJBsfpuSVh68x8hHV01I1yapMLmv2zTL5ar07/z/7ALJ5rkpWVJAdiaPo1FIFycp3x6J4hTseW5+s70zmYTGfRokmz+mpCIqack+HXx11V9zeZLKq1+dIBOSzTe/7SYvkGxda7lck8E4MkJ+INmQbAupSyRbPZHTe3QRrJDJ5uMphrptVrlXSLaOAyVCk/WUbN71p26bkWyu+WuEXgowhBkJmm4yObobM5aGHo1EsrVEtjZNCPf22SAJgFzKe2nSlkAW/lfsWzbdj7bNOiRbw2SDDd2nbOsDJfR7W9sFzpEt02IX5TA/D5gQMiV0cD5O0gdt9aMLTFwmm/FMmi9kE5MsW73nJhSuoN31oytMXMQFynjkmT0zWPCevH43cItsrx4+X19/BNkO9xYJDCDZ3OlHF5i4hkvuQ09FPREgHlgZbJz+ukybrxexe4/W1/97+Cp93qnPBuldSDa3+tE2Ji7hIgen5M9ha4b71ZPJfW8DJCZgTVnvuu+uAmqdZ9RtU9MBhi7JFjIuGalu910EsmQSBkG2rCzYzhseIOCJuPSSVyxSPBfeWdjW199jo+TQNOiqAYKgwJDSLyIJeIs9/VB+V902wfcgwCBs/f1k/zFjcRoC2ZzApVS1StsmxfeqcClMaMX5M6Hx5Miw92RTdRjKg3GnvTQI5dUmt60vi2z5GiFz8QxRaq8IxUvvWqRN0B/Rnqy62HX/Gjhy1DbZPMNlxj+TCFfGBY69lNtREEpBNtW7vCebTo1nn5MrWY1nv7151kv1mQ7UYgBLgw5VweRjLXXbpMpp5J8FoNmCwEUKcKhwKQitWAzmgaN5H6yRrerksMokWJVsRjVeWtlUnZcHWlvVSBog8UxTwu9ybbruT5zsNum31fFxFj39vYi14R0ulHyFPo3Gx7/o+t4J2fKBmdUReUVblWwmNV78TersIiuwCtQsxKufAFWmhapNhRkDJhOl33WVoOsSQkcQHdDLYmciW5C4jI/Ht5SFwi8zvc9rM7KWzSwNIE/YBSd8GP0J9vm71y9+0v3eBKrpkOaibRKOfeGM69OtZstIF2ZkSLhEw63fdbj0KkBi2lDVrTrJiB1ubm7+Y4okVpkrJl9imTbJ4Ir6IrZLRbRJtmVxoZT+vTIu0r6WTVwYJf+qcFHtp+lM20ACJLdXNVVnxenmRfwRpSOer3KwCovfw7PFu+q2CZ43YqPfVJE5n8nWJ1zyz6eaTe0btWC8Ittksn8/s63nK4w80ODvwADDMRN1dAomhboilajnUTVJc5NldvP3VB1irmhTUTsk33uC7xUrpeXT602R7QYmUvRuHmRwDBfRptwHq8QlJ66KPCX/cgr5kPBdfjMNpGuVK2R5k4icryAqh13cfjP/G53uRPEbbdRJ7d8oTTf15qm8AZuZPOVM+zpt4oMaxQdJ8uSxnMSqytp3kWwmTJbAZWoDl9zcs4ZL8bwKXATBTN/t1eFRblKMkkNdVE7lYGNuJOLSNgbek63qXel4vN3mObCGwFzzjWx9wMUNsi14xGYVKZxjsMOP0g3hQEPH+JXCmutWfQG1ytdzuXARNz8DxWWZNudHbC7sHrFpkWyZXR3tyomqHGQ6/GKyxX0Atc6WhMv9yHH5KzRcek220HydHJiNee1/P8kWIi5ItgBB5VcjR3GqyoBAsiHZkGyWRFx8rks3Cpxss1DbjGRz0Hwc0uEnIFcfyRayOFODBMk2Nx9v5yIi2UKQZkL/eLHGUlLe6EWyBafZ8BYbJ4DI72WTk3WL/L48+xyv+UWy1VKXSLZqrabLIcSbRwMhWxOXIWa+B17za2XRQjMyGOELqu1rfkHwAnskG0q1AmpMZSLZkGz99tdu37VndaK4akp6QzZ+KFJ9uBHJ5o9wS09R08TuCxw1JfE8G0rXJqRVsrkclUSyobRmQhpcKuvq00XfDcmG0p4rQD9ri9LaV6H0zFT7Dycp9iNU4VlBmuJGjZBNFGNxKVjiY3Z5yP0IUXixIM3tPo2RTSacrgw3CkrfiNYY2eaNiHahnJjLJwJQUFZRKnEUHehqrLRKNhQUFCQbCkrr8j8brIb5T0AKuAAAAABJRU5ErkJggg==)
⇒ I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
∴
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD0AAAA1CAYAAADyMeOEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAALqSURBVGje7Zi/btswEMaZPdnrQvSW7jbtV1CIIGuByoS3wEMREAgyaCgK2puBIC+QLWOHzlmydvETNEDzBPYzxBUl0ZJlivpjWY4oDrdYosXfne7jfQKz2Qy0LVoHbKANtIH2bgLgpDXQlDo920Y/IQSv0L650x56StAV6Hb/cmCv0utWQG/BG2gDbaANtIE20AbaQDcZ+qPP6pmbF9AAjZ6yYBh1zi9Q9xEC+Iop6x0FyNtj1j4VALgHAVh6f/Aej7SKMzbuIAD++QkCcFU3NE94H4JF8HwvYH+BCb08uJ+ezyen2AIvdUOHBVolCuTDIzK9OvhHhBECT3VCi0RDTNhkPj8VVQ+Sz8HR25ixzlGhRc9l9l2Oe0SVkU2vi7x1tUHzTRA8vI10Aq4gGj2I6sQhwt707+FAeRMg38uRKr3JuoVfBCQlw2/+6xf7TfSmEEtK8GXYq2s/Cd4JUlhfJGtqgb6x4Z2s+sHv0Qwgq0xatfKJW38hW3dwaFmVd1TXu0an9FPQg9uAIjEyFVbvAz6krUkVmTyRBzo8v9+k0OJaCFrkLVEFX6OaIJPQ70ViX+hIYQNofq8vYgP8e+K6Zz++f/2StlY1NsvU/Divt6Ram4TExIba6NqyrD8isV108ZgX2D++EGF7G47qhGzXtIieFr3nz/nhjJ+nlZIV5kdgcp3/tiB8H09cpcCuO/4c9Oi28ETVBushofyoOnHdyVnySAkSFs7OieBAac/lx1/saNtdm0h21fPvMs2ccHCuqNF1uBxichuvQMoMvZmlZWocnvcK7YHLg09k+4RKhLIUudKPCLU6JYh/pYkWc5yeQ9l5LdBl596isRE7Po9PWEc8l7cFH0fTvHGl0EVMeVXB4QYQPm/pAhw8V1VhJXRRU974D4NlTHnjocuY8sZDlzHl2kKrTLm20CpTri20ypRrCV3lCNgI6DymXCvovKZcG+giplwL6KKmvPHQZUy51hNZa9TbQGsS/wE+Z1ZYpYyujwAAAABJRU5ErkJggg==)
Question 8.Evaluate ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAA/CAYAAADXLCfMAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAUDSURBVHja7Zy9TuNAEIB9PfSHlE3H9XiTEioUDKK9E4mV6qIUCK2EKFKgk6FLcbwAHR08wRXQXpMnOKTjCcgzkNuxvc5kYztrJwSvbpCmSGLvz3w7uzOzuzjX19cOid1CSiCIJASRhCCSrBii/PuEhZRrGcQrnx8zxxlLeBMlrHV2QQq2BOJw2N9o8dYPIfZ3Ge/cAFDuXx2Tci2cTgPh7fCW6J212AVBtBRiOKXKKVS0eM8TwQ4p1zKIMKV6NecJLDC0xG6312qJb6RgiyDCVMocd9QNgi2wyLpT/0PWSHEiCUEkiJmBPCnMUojCb56oQJ4CeAshgpMi4b1NMzFsrDsserqN0m8Vg9jh7AagQewnrfG1zg9u+8PhhgbxLU9IyR8IMQi6W67DRhQq2AwxjP3YM0G0GGK8Hk4oD/ofQoS0G3mxZiJ878hlzmhZfS2EWKQCWEe547wQRLPBrjz/d4MYV1KoAp/z4PCQ/SSIZlLGUEpBdHjnzsgKpSPktYM9mk4thah29yGGNIVokgwwSRqYJhSK1GfSHvxc0eSGek6HWLb8xRBr3pMe4M9ZYdvb2z+9dKGSRRAD0d5uMPZLJQPSEggwKHyveQ4Jhug5NoajH/g5eOaA12/D35k76oruLud+kDbAkufiZ9si2C7apni9/6ufI1J+QFZGS68HHJmkzV3e08opVf7SENWGMMrSZB6UimJPZ9z0xQn+jOtIykPfQf5Wb0uHO3eqDngHPuuzBigA4Hi+OFJKjBTCX2Dv07RNuK9hPVpbIoviL/rgSHX6PD+A9xDQyVw/Cpafk3KbL2yZECOBoykaUnuygX+VUqPBMz/isKOlFILDn/A7zRIVaDwd4XJM25QxaMPwK/zM2MOipEioT02Xac5jmfLXBlGN8Ly4M80K9ffhN3ElPkcdlbCllaWtFVgZqXldCc6kTXlWBdbRaLD7Re+renS9ZDk2RctfOcRlkgdJ49Mgoo6BhcRTbDR9M/aspsMiMesyWSn1rol+smDleadFyl87xFynJwfi1LLwetbeRk7LjCedlJXjXS/j4sO7tVrtt8n7ZSGalr82iMl0iCBkT4Hza2IeFOwkKKvSLXeuLLl+mrQpsy/Me5iZ1nPWrMSqtLZnTqcp5YP3Xz5OXBHEmTVKdqY/GGwqZwOfGs/KFOH1C8eleWtuMhClO//19PILdm4Sp8GgTfMeb+Ne927zBkLWgMJw1bpepvy1QUSNfsOxEIyy1BBD/gbrHHRuMOhvYi9SPaNix6nXOdvR2RgLy9TzNGmTPhD1AYZ1lRUGzOhTDha0FEzU98ry8sqHwfhuaTfTYxkwspKANw6s9Y5H8RK4+cqbZK9Nzz+fAe353+H+Bw6e0xQIygIXPTeQN2gTsuzwGaVolMhO2po1taoTEqqOyDmb9q1s+SuBSLeiKrqfaAqRbkVVGGKWR5U3TdKtKMsh0q2oCkLMShXlhQ90K8piiHQrqqoQU3YKSCyBqGI80y0WkopBjAPsSZgJCfpbB3V+WySnSPLBENNSVEXOytCFmopY4jQtxF4h5jMqgC7UVNexISGIJLZDpLXQYojJvp9cCym+tBCiyZkWkopDxGc8SbEWQlS5U9d1HtWZTlKuZRDDDWTXfWy3gx3KuVoMEWd38D0JEksghhvIaAqlO4o2ronxv0uBA65hmEG7H3Z6p+j8JsWINgf7JASRhCASRBKL5R82AcIFLwf3QAAAAABJRU5ErkJggg==)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
[
]
⇒ I = log |cosec π/4 – cot π/4| - log |cosec π/6 – cot π/6|
⇒ I = log |√2 – 1| - log |2 - √3|
![](data:image/png;base64,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)
∴
= ![](data:image/png;base64,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)
Question 9.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I =
[
]
⇒ I = ![](data:image/png;base64,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)
⇒ I = sin-1(1) – sin-1(0) = π/2 – 0
⇒ I = π/2
∴
= π/2
Question 10.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
We know that,
![](data:image/png;base64,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)
Therefore,
⇒ I = ![](data:image/png;base64,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)
⇒ I = tan-1(1) – tan-1(0) = π/4 – 0
⇒ I = π/4
∴
= π/4
Question 11.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I =
[
]
⇒ I =
= ![](data:image/png;base64,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)
⇒ I =
= ![](data:image/png;base64,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)
⇒ I = � log 3/2
∴
= � log 3/2
Question 12.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
cos 2x = 2cos2x – 1
cos2x = ![](data:image/png;base64,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)
putting the value cos2x in I
⇒ I =
[
]
⇒ I = ![](data:image/png;base64,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)
⇒ I =
= π/4
∴
= π/4
Question 13.Evaluate ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE8AAAA1CAYAAAAAjbYhAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAPESURBVHja7ZrNTttAEIC3d7gXxPoGd7zhDSrHVeFIVcfKqVEOUWSpAsmHqDLccuEByglu9BnCsZfmCUAiTxCeIa3H2GTj+Hd/YlvZw0goeMfeb2ZndmcHXV9fIyVsoiAoeAqegleLSSH0QcFjkKFlfNExmmJjeKHglQFn4Avf6xa+/FPwGOTKJqcKnoJXPMDTkvR70fFJ8Hj11xae53X3CEIvMOFIYOKrv+O56XjHSeNHg/MjSBBBrMPkb7dLejQ8Xv3c8HisU0TG4/6OTdBdMJED87E/Hu8slyB5sRzvMGmc63b3fQAzbNoejPEc6zAEueJ5rPq54Q2tEwsj9Co7jsAETYwm8B5ieWeu2981Mf6d5REdgu5pGFTGXftWFv1c8ML4sYjSv+/erzwvK76EyazVwg/EvjpNfdYxj8GocUhZCaOMfm54HYJvAJZjkJ7/oXOtZf6irSxjaUeTj3tU0ayal22L6ueCB1bSEZ4W8bTl5pTfM2FyGOM/eWGCB14R/XzwgmWBn/NgwHPEcHrvEEnnnnnZwjvx5wfnyvn4Fp/w66fBSM/0oNj7MpdtCf1c8KKPKBMXAqsyWhMyZwu3Hrqet0fHNIhPXdfdT4lfs/j/aah0GCmrf6PwIHsZhtVjA+dnvgP06IO/jIWDyyg+nQ9GR6nhAuKX6+7CVqVNtNtwP+fv+8wJxDVW/dzwinhSaMU5fDCL54V7sAU9njrkh5K8kY2SGTwDCc2xT77Bsyem/SNKCDz6meCl7ZdyE4eALNaYumEevDIJIIhDWvtWwSsBjz6Ub6Ka0Rx4OctwJXYQ+25bwAmBt82CMg/dCp6C13h48WpuE6VKeIumixR4vHcBW5ttqQrtgueQ3UTDcMODs2V0Jkwqi/OIbMPU63gWFAj0aVT24RWZhqnl2VZH+kQUPJmGqaXnRVVl4fAkGkY4vLQyd5bYpvld1rKSaZi0RLUxeOCpvFd5VRmGlsHgXDcM8hNj9JxXIcqJMev3okkWgnI2lLjhb7grMAznq8gJyTbMisNo2pOmoacihWBueHSJm7WcXaVhslYdO7zwdkqkxct2K4kyDHhumSItEzx6Em8bVL5ejgRjSOlWqgU8aK8IBpHOTd/r77U1cityayCrW6lyeMtL5HfPWMi4j5DRrVQLz1vegeK5zD2V6G6lvNhKJ50ihQbuhLGpjCb6vLp+mZ0uaUZrBDxR3Uq1WLabEtHdSlsDT0a30lbAk9WtJBIeJBLPImdJbWqVwpPVrSQKHt3tRUva2FrUxZoqCoKCV438B+VfU+IYDSUOAAAAAElFTkSuQmCC)
Answer:Let I = ![](data:image/png;base64,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)
Let x2 + 1 = t …(i)
∴ d(x2 + 1) = dt
⇒ 2x dx = dt
⇒ x dx = dt/2
When x = 2; t = 22 + 1 = 5
When x = 3; t = 32 + 1 = 10
Substituting x2 + 1 and x dx in I
⇒ I =
[
]
⇒ I = ![](data:image/png;base64,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)
⇒ I = � log 2
= � log 2
Question 14.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
Multiplying by 5 in numerator and denominator
⇒ I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAABACAYAAAAnDaPmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAuoSURBVHja7V0xc9w2FmZcx1efM8FWSXovdv9BZsVEcemLVxxVzqnY0XBylmZU+JK1O8+dL31UJWliF9debs5xd439C+w5+Q9I/gta3T6Q4GIpAARAgEtyX/EKaXdJgPjw4XsPD4/R48ePIzQ0NLSmDB8CGhoakg4aGhqSjt1Fo+gDMHzAaI2AGPG23aQDg79Ho5/J5PAIHzBaE4SDeNty0klj8mAJhEUTIJin8e04Sb/s8wClSfxlnM5vI1g3jze0FrtXhxNyFBoEjxL6FZ2k32zDICWUPKXJo68QsJvDG1oPSYf75aKpvvtw9vmQkPj5wZMnH5per+3xCF07nzw5+PALQp59Pns4RNAi6SDpeADBfL5/i0bRu+Wku1oZeS9zK2ACxh9Hv+tW/oezu58NSfS6uBYZvp5MD3fb9vDn6fRTSqJX4B4wW7bz7uzhZyplF30c/64jWiQdfBadJx1XpWALAvh+MfG40eQn6USd0ju6ycdUUBRdlK7HyIdO53faQzjx7dEo/hvvx4qA6Lv9+fyWipjb1IeQqi8k3kzv0zWl7MuT2BjpzGZ3h5MJ/Y6Q6K3tKmIDgpOT/Y/oYOf04OTkZtV3ucqJ6N7Pus9JnHwvTuaYRC8y4pFPaN8AMOoHjf9aJk4goiVhvlepONil6avaaQpvpvc5nE52CxVK6Ks2uramfbHxJDZGOkzKDwZvBoPoDTTQdhVZguB4+ZtjkwnIJhLcg4x+AxdI95uqSQmfy4LLBVkJD1rF/HVWgroyP1dpyv6xcdkgWEJZU3gzvQ9T0xG54DujsIMI6rlNKvPRPt01fWa5J3Fp4kls3L3KQG4HAr6FybYx4/RBlYtRcoVY/GX/5OQj9cNzm3QZuWVKJ2f+M5H5oa3r/1+CzvI+dUiH55vowMBJt6/xi9p4M/yd7j5cFZQ/y+6zxI8Cm00qZZtnZuNJdJZ03GTi7JMkHn+bE9CVanBF4rC5/sotW01o+F9Co5/Y/QSXJeszPZum80+bUDoAMpDJLPA9iv+pAwcnHZV7uY2k4/s+qoVNRvi+1bILfqqe2cqToP+u8iS2inTWyIHHX0oTa+Ui2ZNOBhj6qvw78X4gnU9ODm7GhDx3dV9sQSPcv1B6ZLj3g4p4Ct+8p3GdTZNOgTHJ8y1UcI5LQRUXGxVwvTpq2Tfp5ER5bupJ9IZ0bFl/NWjr5OI64TK3hfxDGQcS7jcakWemSXiyVU6MLdj0G8CeJuN7XOnBNfQBwbAB8S6TjslzV91HhzEZIQlqecH+ny8Wrmo5hNKx8SR6QTqH0/GUuQOaiWQauylcC0vSYQNZEVvi/RSBYxNLqDJTIiv6qCAVWUAcScceb0rS0bivKqUtU8uQyOkyPqFIR+pJDPd+2ZSrFQwE+W+FPBnziZIN/lIGikrHgXRMj0rA9wgh/7UlRx+gsYlbIen4wZtP0nFVywqlfGSrlG2f2ZonsSG1EwwE4NLAoKcT+g3IusEo/tGGLCISvxC/b0s6bPucJt/LBlv8OztS8cWz9FH6x2wVIO9dczJ8kA5TeYo+IukY4C0e36/CW6V7JSGdKve+ID1DtZwr5cu6Stl9x69leTp1QQADNIzI66pOyZicx2Cu7R5YxDMgzwICsuUVA45HUBr/nYMGthNHZPSMX2+1he+2CtiQjqzvLJDNkhvl7mCdYHqfSccUb1X3KdwPdSD5nWrn0IdaDu1e6TyJ7pMO6xR5WwUCIJcB3TmF80YwAWHSwYnqcZLec51wol8vM96XYoILSWU8GMzjO6pzUHVBw448AIDZWavZkPcdngehydMKaYy7V454M7lPFk+8vujoElPZZx7UclOkI/MkOk86/HdVvq2wY8NkJEhiXcQ/i3eoZSFcTy9VV1uYxa6DkMR4PThst+UJv68KWhcEOhr8KN6LkNG/qmoDVa22tsqqL6RjijeT+3C1W1YrORmdlRe8XC3/6kMt1ySdY1NPAhZ2F9fKF4a0N8jSwbOcGZsb2oLAKt7R03iG+Ypul5HM1Nt0sgvJh23OZF7DW76zEgJvJvfJYx4XoFbgM744lq+vUctHLmrZ5eBqqS83xL4AuZh6Ek1iSAfu8knthckqXjcgaDLptrWglcvZK0G9XbWVdJR483CswfU+S6L5uvguoa9kCnxNLefXuB4gNlfLpkpZ6Mu5ri95H85NPYmmMBQERJzpfYO8CPT19BhAlTH30sEXbzqzvGkLhTe0axhatJ50QpBDnu3Zy92bSsKtKF627aSzrYsRkk5gEHC1s20ulu2Og5gqUCadEGU9kHT6ZxIMLXwceA0LgkBbu3yLsk3H9UOrHJvUeqFcK4tHJAn9s/xAop+Diq0hHSzn6s1YTptQxEzEEJuDGV7+53LgtbMgyDOO59sAAMjqNlV2rH4K1IPJqycKdZgLwPgo6yFb5XSGpNMdyzF0tsTQXIWhEo4gE/ul6YHXII3mNTxCgwDfe6V49qXnLgu01j2oaHPgNXQsqSm8bYvJMJSPtzqL2wJHCIIemSqPp+KskXVZj1ZOEsRbExhaaKotGuPIWTLXBYGtPEerHgcVueh2r1zKevgyxFvnMKRUrcKB15dVOCoPzMLUPIBggVbffJCOy0FFHzGdhvF2iXhR2gcSrBzbko6II91CgXK3R1aoltLWsYp06pT1wJhOrzG0KBf5EkjnWOqSWeAIdxP65I8rCjQVZCQAyXdZj00a4q0xDF0jI5cDrwgCibvQZdAUCiSP0UC+xQ4dnOa5FAuWYDg/uOW7rAeSTn+wJWLo7sHBH9gLK7OqCCsMLZ+zwYHXlzIchQVBRzJE19/K0L2V/jposup5/JBfVvKDXIzj5C8AFs1BReeyHq0gnRbiravYyjHEDovCSfUcQ+ccQ/CdHEeXtgdekXQeZ8l3a3V2UKZ3ytqMN5i8iC1UOnqfdsOlHNH6izfElgHpuKazq3ZRQvnJPv3lrN7u8EUTwOhLHGnTY+obbyGxRSP6n23HVsUDgkLoYo1hswJSoUmnTttMViOT19bUNXiV8GRCvyMkeot1YNqDt9DYGsfp/W3HVpVkXc+5EN4FXi0j7cpqOshpp7ZVrQ5JHN8P7XOzSTIYvBkMojdYfKpdeOs8tvbpbtuxJf0nO2U62Dl1TYsPSTp126YDBQDO9fyRi5Tte3GtpsbUF94QWxskHZ7hScjot8n0cNe2w1yihjhAaNI22+JC5feQA/gmk/RPtitkE68P6aN5wttZXbwFxNYRYktDOpLi1Vfwfqaq/ALxoWe5CeS57zwPk7ZJi1TF6QNdcSExb8U1RwVJJ9yYNoE3S2wZF65CbFnEdGaz2SdJPP42H4irqsQmeFEc6+Rw7wfIeN0Z0NNQUfqqtvkoUuUSC0DSCTemTeHNAltrrxBGbHkgHfEh8yI9qt0Bibowfl1NHdO1TVZcKIT6QtJpbky1eAv15hFDbNkUQEPSsfCZdW9hgKzebHUgF01sOZu0LVSRKplfL8aETHMkkHRq4K046hEOby3CFo8J3egDtqzYtq1v19S1LUSRKpuyDjowIum0H28G2FoEwNZln7FlGWhrZwq3rm2uRarQvWrvmCK2tsC9Kjph+N6lptOvVW2rU6QKSWez1ha8qdphW7gKsaUhHVWuAewWmEhdNtFzX9v3INi0rekiVUg64cc0JN4csPVrR7B13HrSgYcM9TOg+E6WzHRwM6Hk6ThJ71VdTMyXYIE2yO70mPZt2jZNcaFgRapsgQHtmU/pHbGi3zYe/PSON8fYigdsHbUYWzfahK3rgaxkfE9MkoIiUKa5B4xdhe1FyPD0mZVs2ra1IlX51n3oIlVwfdM0AUkiWiO1hNtoyzH9ug14M22HpgDaZYuwdd5mbAWVgS6yEA0N8dZzlxpBgIakg4akg4aGeEPSadrHRkNDvCHpVBrsJsAZFNi65DkyWOAcLZQh3pB0mK12ZrrzChO07hriDUkHDQ0NDUkHDQ0NSQcNDQ1JBw0NDS28/R8Y3PAGygOO0AAAAABJRU5ErkJggg==)
⇒ I = ![](data:image/png;base64,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)
⇒ I = I1 + I2
I1 = ![](data:image/png;base64,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)
Let 5x2 + 1 = t ….(i)
d(5x2 + 1) = dt
10x dx = dt …..(ii)
When x = 0; t = 5 × 02 + 1 = 1
When x = 1; t = 5 × 12 + 1 = 6
Substituting (i) and (ii) in I1
I1 =
[
]
I1 = ![](data:image/png;base64,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)
I1 = ![](data:image/png;base64,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)
I2 =
[
]
I2 = ![](data:image/png;base64,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)
I2 = 3/√5 tan-15
∵ I = I1 + I2
∴ I = 1/5 log 6 + 3/√5 tan-15
∴
= 1/5 log 6 + 3/√5 tan-15
Question 15.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
Put x2 = t ⇒ 2x dx = dt
When x = 0; t = 0
When x = 1; t = 1
Substituting t and dt in I
⇒ I =
= �
[
]
⇒ I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP8AAAA1CAYAAACOez0YAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAewSURBVHja7V0/b9RIFB9SUEFHA8dsF0B02dn0FGhx+FNGdxtrK04posgSsJKL6OKki7g7eqgSqvAFuCJ8AfIFjtOF8hqSr5DkPN71rtfx2DP2eP7YL9KTiNiN7d97v3l/5s0z2t3dRSAgIO0TAAEEBMgPAgIC5AcBAQHyg4CAtJT84c+1WACwCkADjqATW8hPAdnYWO32+2QbY/QP7m++AYMpZ2CAI+jEKvLvDMkz1Ol863TQtxCsSzDacjLB8W/AEXRiXdi/45LntgJkUkhnM46NXQRarpPGAkRJv9ZFH025byA/kB/Ir0g8B78O7/sCyA8COmlh2L/Zx2+A/CCgEwXkD38WWFJDLs+61rUmkr9J21FQh2kY+YNgeJsg9D387PlVwT8cL1iSHNJnXGc+zG8K+bc2Vu85rve0KUbnuc7T1Y2te0D+BpG/i7pHwyC4bUqY3wTy+/7wTq/nvF3f27thkWfPjfb29tZvOL3e26Hv3wHyA/mlhIdNI7/vr9980iEfdC6o4lHK4y5G6DSM9k4fb2x1mfbiOUsYO5/Wff8mpGJ6Uiujye/1ya8i6UKS7PThw99H4e8jE5RUxtAm92+NV4o8OsafqM6iNLDz5EMeuV2C9skgeGEb+ak90cXLcV+tmKqLV66zQhffPNs3lvzjfXr8rugBWORP1gWw4722jfxjPPGxzFqJkmckawfx72sEHRB353mu90fdY13hf0InI9HvLTveS9P14RL8B11cWfwpzN2CAaFfvkTdtY/panqd5J8o5oIKGe48KxP2m5QD8+I4xZN+/q7zxaZcXzTtiiKFu+iLDu9fRifTtAavHJqil7zDSRTfFYwPWekXyl+V0Y90RZ3lRWWT3/MGS3EIWdb4TBBRHJOkSHrRJpI/jg5UL3JldDK3WOVEMypJPzmc9Fve4aToHAPFNyP9kgeoZPIn80ebyV/BOM9se5Yy5KefQQif2ZDemBSN8R5OmmzBn2RFV0B+U40sVKgJHkbYIAVy/mTerbPwx22PUTTm7htXZymoJdHCapb3l0j+Rw9voVv/PQqCh4L5ykJWvhWTX6TgN3xw/eD6g6FVoTIzFOb0hnkY1phjMnUW55i8uXEc5Zie4sT3WbSYqdYHD/nHn8Fn6dxfG/npHrbT67yPO/MQ7h6nu76iFSv8f96CXxPIP/UwiHwviqJ4MJQpPNeb5dN8XZ3TzlDDi5s86Uk2Pv593eRPpJEj7eSPutYw/iveJw28wSLNSyKDr7DtI4P8BecGmOcIZKZP4zbpfPJPMPwct/3KwlD19XjIr1sns2iMrRPV+ihB/tN0dKWF/BTISfPNVGm0oaVqq6UM8uecGzgXrQ7XSf66MFR9PZ7n1a0TnmisAJ+RVvInF9hE3q+c/DMgoz38qwqsUFBpQtg/zYFzPGEZDKt4zzp1Nvvb5lb8i6KTYnwG+3VFNALkvxKFpG9mQUTKkD8Gsg7vZAr5RXFMYslD/jIYVvGedepMFfkr2XaBThL4CHl4GREND/lZGKcBOheRKuRnVXer5Gym5PyiOCaxFCF/HRiqvh4P+XXopAz5aaegCn3UQn4VYf9cjpcqhNCiCSFu0Oqcn5/8J3VgqPp6POQ3XSdJfFZ9/6cMfLaB/BOZbOFdxltFyQJJlcaWRuT8nAW/eQz9+7IwVH093uc1QCcnefeoWh8Z5B+JFiy1kH8GZlQguZxI+G9yUsUA2rTPXxeGqq9nwz7/nE4Y23aT5/hXlT7iOsbscNIvzMNJLIy1kH8cSg0WaTdYHK51es77qspvW5NPHRiqvp4tTT5jz55flFSpD+bhpIzwn1Wz0Ub+OqQp7b08htYUmbX3mtUzn113uNoiaxPG6YVBalho2gy/ZHgke4JwnTI97GLZwZ4mP2vcJWf6ASQ2xvg07UyKcoq5Qwp5Wxamkp93plydIoJjMkxrw2BJXUd6RXUyPmiGjmybsUAlak3GzlE6BWF+gY6LDllzPC1e4O5xf7D5TNUkHxnkz5wppzivFMXRdkOTZZim6STyoPTIMi3gaZ46LCJ5A0gY4MTecjYPPwaKFfaYSH7RmXLyjUwcx7l7t2yMl0zDNFEn8aJsU+gf2RFjcWU+IHbc7fgLtIoZeaIIpOwqtA1z+1UO+yiL43zoj7/aWGASy6PJV1U2U6CTC74dFjpyfOVQ58hxXqFHjOnuA7NzMuvhsiaTFnViAfnl4Hhl1W5w6B/pQ+FkZRk6if8O7dozfW6/5yy/zIuqxPMz8Pxy8lwOL1M0fdVmic6/d+rtS6hDJ8kFwPS5/UULmXB+xtqPjclPe5t1vagz/ZIL3Tl/GRyzcLXtdV1cGNDXdRnSzmvqfL7aowOxQgk7P0u0N+p8UefcwY4yM+XUFJzE8twoLzXYy5TxSgMvWDTlfsropDXkj96eQ/CfvLP0zCsq8c+UqzsPi3BsQfOONQRosU64wFFdmGmqkQGOoBOryG/Le8lMF8ARdGIN+emqSHOhrEEEJm9xmOhdAEfQiTXkj15BPCAvcHftXbqiTlsjCXF+b3LnmUwjAxxBJ9aQP8qDBsuD6JjlbCjBnLThwImUfBJwBJ3YRH7PXf45f06a/qq5DQI4gk6szflBQECA/CAgIEB+EBCQpsj/txCVlAeCrMwAAAAASUVORK5CYII=)
∴
= � (e – 1)
Question 16.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
Dividing 5x2 by x2 + 4x + 3 we get 5 as quotient and –(20x + 15) as remainder
So, I = ![](data:image/png;base64,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)
⇒ I =
= ![](data:image/png;base64,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)
⇒ I = 5 (2 – 1) - ![](data:image/png;base64,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)
⇒ I = 5 – I1
I1 = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAABACAYAAAAtWJjYAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAX3SURBVHja7Zw/b9tGFMCve7zXQU5TnT06+hsENJs/o4tIhKcGGgSDQGsDGtyC9ma0dfd4SjZ3yNoOztgl+gQJ4HwC+zNI5SN59JG6I3nknUSmL8ADbFkK773f3fvneyZnZ2cEpd+CRkCIKJ2FGP37hgsaqYcQz88nDzxKriOAC0LYl4PZ7CEaqmcQA5e99oLwCXw9ZuQdeeR9mJyfP0Bj9TQmhoH3hJLh/CAMt9FYfYUYHmwPyfAaIfb8JDI3eI2G6jFE3/N+tBEPxey3Tgbch2y57tqKupvQSfmDQ5ceMf/0hWllT6b7j4eUzKPFL2Ohw7k7OnyuXMfIfZ6+fwHvfTo9GXYJ3nS6P3Rd9iul5DN1D4+qwhMj5Eumeyz0jieSxiDCzogAHkcLOoavZ7ODh64b/GAG4NOIB7lLypdMYmXYKHy5ovSIvYyV9INncebse8/g87L3bkJOffaCDAafBgPyCXSogggHo6D7gjD/rfGT6DPyNv8gett2p2T15yPygXp+yF10GIx20pp0GdekQgLFd23RMIkh8u/tBMwKiHAY2GDvcjKbba01JpoUVZLE4RbdSgJr1dUkZQ+54wZTxZc2MQeeXXWqdCHGNTe8hzr/QPgwGd87sZMTBe9PVwZW0mjI4gobv0u/vhFjDBgy/7q+JzENMd14t7kQEsV3U90wrWzSBsAMmBAbMlASiEXA8H0aApbi+xPDsptREO504SQmSdD0O9/b/SkFujTV1qxWaLQ7SpORpY5iOm622BXiLhNOm9r9Fk5uGlsh6ZnNJlsepX81jeW2IOZ04LmAREejENPFCVlk+3R41ZXSi2IpowtROL038Lrj0Cud8qgYV8XsvE5s1YVYXG/bJK3SwAANmuLgAgaO98Zk8a/a8WLcU/5M4mq5MXWa9tK0XyGqjdEEYlnyZgxi0jelc9MnT1Rc1dKrm9jI/k9K6b9tXb9td1oWSsxCjB9AP9uAGJcbzA/LWleqepC7WqkLpt9fBafBt0m8oXdNuzvrghh/jnrXbb1b5cJMt96gC0PZ+KIYb6Adx5j3+30jIF8PFuDeiHChkHaoc8Vfy2Jqw+zPNERZTIXvebiyltjYgChmujKRA6O3cKJA6cDffQWxWVxTnIlCJyhKRAqfPebxcX968tgWRFhX0h5MMk1ZAgSwBmzvEtaRtDInW/Darh+8slonNnURKgEA5YmDvCjn4JIGOPtYrPvENiFf62qyolfw14UoKeJz65DqEAkkiE3qV22IqSGs1IYoa+qdcogmilEUhIjSGiLedkOIKBuEyH//hRARIkrXIcpubqHYF9MQFyjrF3SnmJ2iIERJLEUIPezY4PzjVwAR5x+/Aoii4PyjZYjZpSObEDsw/9jVuKwzObVZiBuef+ziXEdil9EOo+RjVhvS4bzsdkKFq1u942JSbM0/1pH7Ca1uQQS7O473mzh0lABVr3NjEG3NP9Z249mMZHcgxpk7835ZuaapuOFXDTG931llaN2pJFPzj7o30kSBS0owYie7SW56yqrNOhtBFBea1HPl8wxNppJMzT82NU58wZiNL2TjADamrNpCTK42RqVYyTDqyg6NFx4pOQkn23sDdlnlamxMJdkyDsDg91NVMx2m9WkKEeDBKHns9h3vfdlw6or7FHbhosmUj4mpJFvGES/rqiCa1qfJOvNdrWSYiQ7Hfyp/m1TspiT3I+mtburfZiqpSd2kO7lUNGYZxDb6SNZ5pLPOIkzhzqr6hrlJQzeZSqpfzzWfXIoTg8LoAL85zvu3MsPq6hN49Oe2E1ZliY1qwxmHaGIqybSbKtkEWegozneY0sdEdpqEgvxIfC2Iuqm0yamkdRin0p0a0scUxHgjKjxCKfm6Dzc9lbRpiCb10V2nLGZmfz5GJyZy91Pn4TamkjYJ0bQ+OuuMW2xQIcS90ulQnKCizP9Du3da9+E2ppLWBjF2k/lYaFofSHa0SjVn8CY3YUWdv/lf1LIGEWXzghARIgpCRLEO8biYoaH0CKKYjeFp7PFJREGIKAgRBSH+z+Q/oOZPiiXpX2oAAAAASUVORK5CYII=)
Adding and subtracting 25 in the numerator
I1 = 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)
I1 = ![](data:image/png;base64,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)
Let x2 + 4x + 3 = t
(2x + 4)dx = dt
∴ I1 = ![](data:image/png;base64,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)
I1 = 10 log t -
[
]
I1 = 10 log t -
[
]
I1 = ![](data:image/png;base64,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)
I1 = 10![](data:image/png;base64,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)
I1 = ![](data:image/png;base64,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)
I1 = ![](data:image/png;base64,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)
I1 = ![](data:image/png;base64,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)
I1 = 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)
I1 = ![](data:image/png;base64,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)
∵ I = 5 – I1
Substituting I1 in I we get
I = 5 – ![](data:image/png;base64,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)
∴
= 5 – ![](data:image/png;base64,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)
Question 17.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
⇒ I =
[
]
⇒ I = 2 (tan π/4 – tan 0) + � ((π/4)4 – 0) + 2 (π/4 – 0)
⇒ I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
∴ ![](data:image/png;base64,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)
Question 18.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
We know, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMQAAAA1CAYAAAAeaETXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAYUSURBVHja7V09b9tGGGY9J52bIOct2aOTxnYylMvX6KYU4aUGNBgC0doGNBi17M1A6+xJlqRL/Qs6NBm72P/AqPMLrL8guToejzxR/DhSNMWjHwPPQlH23XPPe/d+kbaOj48tAAAEQAIAwCAAAAYBADAIAIBBAAAMAgBgEAAAgwAAGARgzX6+iSJ6HTwtxxOEZghGo60H1LKuZos5neGGgzB3V7k+u0aumTt6Cp6s/+Z46g72dHmC2AzCyUn/nkOtj96iPmJf+icn9zwR2PS1ZdEr2x09Bk9zPE09nobD+/z6kUNfZfEEoRm42IxYn7lRUHv0ejjs339OyNldPxnK4gnkGe0+0a/tNjmjztEr8FIOTyCuJsFf3u+K4993nXyXADwl8jTV5QnCXBH4Ee4f6RO+g20Nhw9z7X6zuIEQ8q8fNO6Dp2SDyMMTxLkiuKyzLf1ZLwBUguQsHOxstAh5fuYeud8JsZDxxs5BCzwtzxPEueQxXoqv67KnxGpdbI1GD7J3zK2HbdI+k/eK71rXRXZP42KC/Dz9lZcniLsgepSc8h2njOyOCP7oP1kL7bkPj6wv/OhXi02DLtmX8cTmzsGTZgfJt8sTxF0QDiV/lFUI47tXh7nb2X/Ty61PeJDIi3LCpSC78ppAc4tzhXjqDvby8ARx18D1chjb1vWLwdPt8gSyV7zIs2N8T+bH0Yu0ep5SA8a0wDGpgSrtvqTJ1LFpLWvcceOKXksbv/RpfT93jQeB3a77o2lJhdvWSNU8xaSqNp+0Cflb+lrr9Nn7aEGDBy0O6/wqonbhj5FW723cfc/o+nvvHkLP7R37B0qd0WKgVK+mtaxxc45mn38gFrmU4+LfsRndJcS65K0CrsNeUGKde34s5yZy1Kt+rmm+v6KRia+RDxkamWhoZBLHddU8RSa60ZpNYNxx3DdzqSol9ysjeIuwz/Ka63TexFUDe9T6JIOaoOGK9j5FB1FG01rcbpSG9AxS8rg5J4qhjudy5L5R802EOe4Lfp0f9V4/TUPaK3yNXM808lOVGqns5FNF6U0iMhiRTaFXMtUlFngx3SgXXk7O3+G/8t1y7jSgzmHcQJZtWvOzCFMdyAxNcmovfdwBVxEe4sTvC2YseTEZJWpkP8q13KTSNFKpQciFS9vJAkJiqoXy+/KzUOBk3LUHL3V25jo0remOm+9seQxilbteWSdpHTRSmUHIZrG0yUqLjp2s/IxXAv2dIjgmPV+cXHbsgZ014To0remMu0qDyCviNGEt5uP1T9K6aOQ2eVqYbFoDVNpkQzcinKwQhP2YtdffBUFzq/dn6ilRsGmtzBhCZ9wVG8RE1x1UUfZGUaVGihhFGTwtHmcpvR5JvvMcEcrCq5Pik/azLok7zDJNa2XFELrjNtVlWgbaGklYuzI0Um1Q7Qe13EK5uyJ3U75rywH6wrtR+0TUDJW8j/++Lu3+pro9aT5oXZrWdMd9Fw0iqpHNfv9bXhtI0Mg0QSPXRTVSqUEoR2JQD5CpRTV9ppAylf5ekGajzscoeYT2TqVxieaqMBuh5qLr0rSmM25uvMIXFhkxuXEIIwk3CymUJj3Ic7RFXxbQyFrwXEO6RtbEprKokZUYRJBn9wtKXtGlzd5F6wAiX8xTbWGxpMOcX1Sf0Zssc3523Y3vg9/HCy8xNQUlhx9tWptWXbjKGnd4cqkumHMYPsQSzmMhgFVEY7rr5HMz0dDIJIdGJkkaWZlBAMBdBkgAABhEAxYuZxoZPOnxBNIMBG+uaxHrIghqSeuCV3rBjR5PeJVloxZZpC4jtZUbmfECR8vxBPIMQpCmZM5h0BHMq7yyNhCpAIOn/DxBaAYh6ZnitA4C8JSPJwitIRBFQZwQy/IEkpriIkQ6BYBiPIGoxgSQ9BynQ7YrlcUTiDIcooeKnOIN4OXwBLIMB2+Gy2pnB/R5AlkGg3cn67zJDjzp8wTCDI4b4h7GRxvHYtyQhyeQZqAv7D1m2+q9lQ/nSPBWBUrZ73gtZnGeIDLDFnlgd2zxGKf6gE6IJrzuZpU8QWgGwX9DRcqD9Pi3vMvyBKEBAAwCAGAQAJCJ/wEEY/fXpJ7j/wAAAABJRU5ErkJggg==)
Substituting
in I, we get
⇒ I =
[
]
⇒ I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAAXCAYAAACyJSuuAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAPXSURBVHja7Vq9UhsxEFZSwwPAIDro8fraVIxREigZcr5xlcSFx3OTADNXkOSg80x++gwNUCd1CngB8gbMmBeIeYWQnO4kI9+v7TvpfEbFFj5bWn26/XY/rYxOTk6QNm2P2fQmaNMkmHgAQk+ozf3GPBKc2qYgQRPQOUL4jtjuxjxvjCycnFxlEawM/7OOeeIJLUBnXnAM5p0EMnAedTZrgNG19zL+IgzXm52jmkpMZfifRcxhMuhyqMhcE3a8zb83LPsV/Wxbxh79DKa7M6/+q4JZB6gCc5zWMiB0i6B5Hq02cNtynOV58182ZtdtLY3rP1U/8bIhlo84bRV+VrYGnFQnysbZbeAD7zf/wDreFp8fW7BNn+NG90Am1jL8VwlzJDC6DXiLERpQPWwQ632ns/kMGvabQF/trm/B6ilG+IZrZcdpL5oE9jFGN9Sha5MNpsHuca35bdJgjDMZBCgaZ9I6e732AllBV3GHbDqHt4a7cLYq0srwXzXMUfaskKt2r7cQDDDXvJLSp6xhgweURXxy6ux5Hf2ggeCzDshnYtkv0pgYPrTUMPodzJlkxXdopOBM0LnDspz2Qmh5dt0lqbJAof+qYY6wxwuEw3D5wMTeT2NY0E4cDXhedpIYzxbaZ4GVYsV2aJTjTHnpDy8rPiDGqZJZFTOP/6mDsGKYY0oI3O52jtbjHCQFR1zWzyp7NjFe86DzfwvNryPBJqlcqsaZJyBsgvf91l5movAkGdvLqpNgIswJ54qpSSAswC/5GNd/hYOkyOCIZGEBUBYJ8mYLlThTX4gKaTCl/zx7XDXM8Rk60MR+kKzC1mnbcRZlkoCO5yQQ5Epi90AI4qkzpCqcaZlvOFY4n8jTx5P5z1OFqoY5UTJYxHg3PCCyAbJIQDM/HzsOCYqURrJx+nNhdBl3SMs6TxShj/P4zyU5K4Q5soA0bSyDBPxSJYkEslqkKnGyrBrpIGV10Io4E+Txn8eUYM5WC2P5HwmEBjQ+ckkwOkgeCbyxh+J8Qx+15gVdC+3nF90dUo1z2AnzMIkXc0G3CfqytHGZ/quEOZoNMbnkB0V6aeQ/A+tMzNo0EAyza9Lf0EskUkc/2S3cIS9T7H8bgcQIBVykNHk+RX0YXG2ze4LQd4V1hxTiFLDes/meMtINZGThWfF/3IKXpWIe0/9ocAD5YNvmBqmvfuc9egzWFxqEwiWSUIKtT4H2EsqUF0jRg2s88/mc4UU93MYW/2/VMnAOS7Rl7LG5/X80mra7piIYyvTPfP4pGXOqf6RyQdq0zaLpTdCmSaA3QZsmgd4EbY/c/gMDDTUVCohwJAAAAABJRU5ErkJggg==)
∴
= 0
Question 19.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
I = ![](data:image/png;base64,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)
∴ I = I1 + I2
I1 = ![](data:image/png;base64,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)
Let x2 + 4 = t
2x dx = dt
When x = 0; t = 4
When x = 2; t = 22 + 4 = 8
Substituting t and dt in I1
⇒ I1 =
[
]
⇒ I1 = 3 [log |8| - log |4|] = 3 log 8/4
⇒ I1 = 3 log � = -3 log 2
I2 =
=
[
]
⇒ I2 = ![](data:image/png;base64,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)
⇒ I2 =
= 3π/8
Now I = I1 + I2
I = 3 log � + 3π/8
∴
= 3 log � + 3π/8
Question 20.Evaluate ![](data:image/png;base64,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)
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAABACAYAAABodfcfAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAfGSURBVHja7V09c9RGGJapgToG71Ux1NzaZZKGOeQYykui01wTJld4PJoEe0aFE2R3Lmx6oAE3cfIDUoDpUgB/IMNgykxmjP+CfdG72j3tiZO1u3c6rY6XmWfG3Ie8et5nd9+vlZ2dnR0HgagTkAQEihaBqEy08b85AJJkQCpyN33RAuGdpnNAWusbSJK+YJG7CkQbuORBTP45Eq8P5K5C92C9RTaQeDMgdyhaFC0CRYuiRdEikDsULYoWoS1aSNvExG/GxG9ivlGTUOSuGtHytM0ZgLjBAyRKHchdhe4BYqZ3g0sGmMt+F0WLmAq21to3msR5G4uun48v/1t0nH+hSMJfO4ddI4q689RxjpPXyIkbRLesFC2vow/NNoS6f2sTd7u7vcsucV4K94WLUv6Z/5++96Jg0afOM/bagvuqF4ZX4BqRR+/F7x97QbRo5UrLggpv2SOOcwqzC4ILFKNGQGYZd9tdukpc/2Fvd/dyFLi3CO3sD8S84BxlMx6SyPvUi+6FYe/KCiGHVa2wSqJNZtVgFsKW8LHqAdcF2z69azN3bHy081wWLfW3736igYFLQD8sLZHDUZ+xSrQdSvaB6MBdvh+vGCeNJfcxzFIUZTFs5w5EK1ZWLswPeYLkE3DITbBStHAjTYe8xZVVH3XgjueSN1TGCzsuIeRv3r1WuZuTTzz4PA55h6I1EK3l3GXdASHa22tbTeGPp9mG201CVg6D7eCLxL8lp/HnqJWi5VtCv2wfRoqw53SibN3PV+DPjs2duMeJTyoWq5BTMamEewCraK/XvupTGnWjaD4Mu9eWyNIh/JxORucj+LfdMLw2jq1rK1opOj2nrvsrEKJSRUoi89Yq5BttrPFPijvwi2VxTW4XgIwGPRZilLMEDNR/BpkCnlHYlAoLrETNPhP7t+218KZeNmUyNiskvmxRJLOcvmhvtZutVvCdynfE6YBpjG8c0Y47Np+SvUkn8fmq+j67OLB0WBwwOoS+hhwsz9EOlaPlEnUC9bFJ3+2XJlroVJqWKBIj620505pUhkHOhq1jm4XJXEi8yOWVutp67jeNhvOPzs1MQ7Smp2qnyR2KtoB40yaKTDlz6DMsOqWd/cSvIn+KCDbnOoNrZAkoo8HDtC9WVbQyL9moPS8QywSu1pfYL7KZqd2KiV9wj1jZj/tCuk0UzKFfajwe+EGk+ba9tnVjKACIHX8eIMQ+lftyVBIeGj0ocd4k16BvfJ/+JAgwHVvpouXcjfoM8HKHNp6I+/HWvK8p9SP5fuP3n8qpM/iO59IHhDjvoKwa+O63MSev2f02O49sSPyr2kz2r3XtpkU8iEyniSJJmZC/XP+XlSRy9RZFSVDHf4XrsJTMoG4eXychY0CA7tiqFm2HOs8/GTtfmWECp8ZMsweD+4uvDRU2wSsPcvo2lFh1bGZqtwvSLc7zUcTrNFFww2zKS71ImeiIAR5+kV2BRwU7k27wMBVtHneZCP4DjFFsh+w16j8cupcF5yib8hL3LQtUpLFsCvwYBwo2M7GbEfEqTRQp6UPtbylil0Anr5i90Tyn3rTBI+t3iwmWnXQq/mORaFMjkdOWt76ad83kOuqitSXw07WZrt2MiRcDyGuikKosY83+vBu9iICisRXkEc9G95imoN3t1XFEy36fv/z94HcQ8m7ZW/eywp2UaA1PKmhhXJtJ7xc25phvcQVNFEK0FxA5V5ZoJ9XgUZZ7kIrNW5SC1L7T7BzIvExQtGdlYxKiVbWbEfE5TRTNkaIdEXQxJ12KlFVEmzVIHgEqY7NBtLI45SBFFmNd3YOBzeJJqCpancYc7QhYp4mCR4X9JM0V3pR9RVVfU/Z15OvzBvWh1WnSDR5lZQ/Ap23R1m/yFiiENwuiLbbZDweyS8Ht9ruq3bSI500Ur1SbKKR827l0cO4cziCJAWr4m+DrHLV7vauQ/+PbanI9iFKj3rzO2KoWLawmhPp7cD9pViVtYgnD9vVkp0oialFMYJkUfnxHvDYQgyVN2so2i7kxaczRquqYNFHA1gfpC/G+aQe/OAEgrpEEMuRk2fV/hutNusFDfN/k2QVFFTEmWtf/MQhuf8WLA2eiUUVaaU7ksUO+M3Mokd3nJ/eYU5ypRrgX2ww+4xnYDevnJQC5K7k0jMSjaGdGtHlRO8I841E7cZR0cgJFi6Itc8fYZBG8RtBcqWhtrGfXBbPAHcubJsdyULQoWvvBij9JseO8XqIteIADYqeIu+M6csdywZTssxQba3iyXLRyVzw/SfAHPvdAL2ipO3es/k/9vbRLz3LRdprkEau2sC743rU7DfrEtgHbilngTi6n1kK0w0cc0qMPKEh1d6DO3Am3QOwOtVlp07IblNqC+yhIddSdO9ZnIU202ogW8RlnO2K3Rm7qhscjCdG2w/C6TUUGNBoi79SG9Gzd5Ongtqy4F/k4l2ws4dXEP6w9d7VzD3g15CP4Z6Zd/58rOHcndeeuVqJlTbk8x8ii4sadJ7Y9BMJqQ88Id7USrfwsfgAc+cCqmBpmiTsQ7QpxXtjky+aKNnvEBP/OqzqQOxQtihaBokXRzqho0acdw6ft0lXkrgLRJg44OYR0jXiAAv7tMJ3ghXFHkbspihaQHmGu7o/21hXIXUWiRSBQtAgEihaBokUgaoT/AY0m0PObkpVyAAAAAElFTkSuQmCC)
I = I1 + I2
I1 = ![](data:image/png;base64,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)
⇒ I1 =
[
]
⇒ I1 = ![](data:image/png;base64,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)
⇒ I1 = e – e – 0 + 1
⇒ I1 = 1
I2 =
[
]
⇒ I2 = ![](data:image/png;base64,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)
⇒ I2 =
= ![](data:image/png;base64,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)
Since, I = I1 + I2
∴ I = 1 + ![](data:image/png;base64,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)
∴
= 1 + ![](data:image/png;base64,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)
Question 21.
equals
A. π/3
B. 2π/3
C. π/6
D. π/12
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
⇒ I =
[
]
⇒ I =
π/12
∴
π/12
Question 22.
equals
A. π/6
B. π/12
C. π/24
D. π/4
Answer:Let I = ![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
Taking 9 common from Denominator in I
⇒ I =
[
]
⇒ I =![](data:image/png;base64,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)
⇒ I = ![](data:image/png;base64,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)
⇒ I =
= π/24
∴
= π/24
Evaluate
Answer:
⇒ I = 2
∴
Question 2.
Evaluate
Answer:
Let I =
[
]
⇒ I = log |3| - log |2|
⇒ I = log 3/2
Question 3.
Evaluate
Answer:
Let I =
[
]
Question 4.
Evaluate
Answer:
Let I =
⇒ I =
[∫sinx dx=-cosx]
⇒ I = - (cos 2×π/4 – cos 0)/2
⇒ I = - (cos π/2 – cos 0)/2 = - (0 – 1)/2
⇒ I = 1/2
∴ = 1/2
Question 5.
Evaluate
Answer:
Let I =
⇒ I =
[
]
⇒ I = � × (0 – 0) = 0
∴ = 0
Question 6.
Evaluate
Answer:
Let I =
⇒ I =
⇒ I = = e5 – e4[
]
⇒ I = e4 (e – 1)
∴ = e4 (e – 1)
Question 7.
Evaluate
Answer:
Let I =
⇒ I = [
]
⇒ I = =
⇒ I =
⇒ I =
∴ =
Question 8.
Evaluate
Answer:
Let I =
⇒ I =
[
]
⇒ I = log |cosec π/4 – cot π/4| - log |cosec π/6 – cot π/6|
⇒ I = log |√2 – 1| - log |2 - √3|
∴ =
Question 9.
Evaluate
Answer:
Let I =
⇒ I = [
]
⇒ I =
⇒ I = sin-1(1) – sin-1(0) = π/2 – 0
⇒ I = π/2
∴ = π/2
Question 10.
Evaluate
Answer:
Let I =
⇒ I =
We know that,
⇒ I =
⇒ I = tan-1(1) – tan-1(0) = π/4 – 0
⇒ I = π/4
∴ = π/4
Question 11.
Evaluate
Answer:
Let I =
⇒ I = [
]
⇒ I = =
⇒ I = =
⇒ I = � log 3/2
∴ = � log 3/2
Question 12.
Evaluate
Answer:
Let I =
cos 2x = 2cos2x – 1
cos2x =
putting the value cos2x in I
⇒ I = [
]
⇒ I =
⇒ I = = π/4
∴ = π/4
Question 13.
Evaluate
Answer:
Let I =
Let x2 + 1 = t …(i)
∴ d(x2 + 1) = dt
⇒ 2x dx = dt
⇒ x dx = dt/2
When x = 2; t = 22 + 1 = 5
When x = 3; t = 32 + 1 = 10
Substituting x2 + 1 and x dx in I
⇒ I = [
]
⇒ I =
⇒ I = � log 2
= � log 2
Question 14.
Evaluate
Answer:
Let I =
Multiplying by 5 in numerator and denominator
⇒ I =
⇒ I =
⇒ I = I1 + I2
I1 =
Let 5x2 + 1 = t ….(i)
d(5x2 + 1) = dt
10x dx = dt …..(ii)
When x = 0; t = 5 × 02 + 1 = 1
When x = 1; t = 5 × 12 + 1 = 6
Substituting (i) and (ii) in I1
I1 = [
]
I1 =
I1 =
I2 = [
]
I2 =
I2 = 3/√5 tan-15
∵ I = I1 + I2
∴ I = 1/5 log 6 + 3/√5 tan-15
∴ = 1/5 log 6 + 3/√5 tan-15
Question 15.
Evaluate
Answer:
Let I =
Put x2 = t ⇒ 2x dx = dt
When x = 0; t = 0
When x = 1; t = 1
Substituting t and dt in I
⇒ I = = �
[
]
⇒ I =
∴ = � (e – 1)
Question 16.
Evaluate
Answer:
Let I =
Dividing 5x2 by x2 + 4x + 3 we get 5 as quotient and –(20x + 15) as remainder
So, I =
⇒ I = =
⇒ I = 5 (2 – 1) -
⇒ I = 5 – I1
I1 =
Adding and subtracting 25 in the numerator
I1 =
I1 =
Let x2 + 4x + 3 = t
(2x + 4)dx = dt
∴ I1 =
I1 = 10 log t - [
]
I1 = 10 log t - [
]
I1 =
I1 = 10
I1 =
I1 =
I1 =
I1 =
I1 =
∵ I = 5 – I1
Substituting I1 in I we get
I = 5 –
∴ = 5 –
Question 17.
Evaluate
Answer:
Let I =
⇒ I =
⇒ I = [
]
⇒ I = 2 (tan π/4 – tan 0) + � ((π/4)4 – 0) + 2 (π/4 – 0)
⇒ I =
⇒ I =
∴
Question 18.
Evaluate
Answer:
Let I =
We know,
Substituting in I, we get
⇒ I = [
]
⇒ I =
∴ = 0
Question 19.
Evaluate
Answer:
Let I =
I =
∴ I = I1 + I2
I1 =
Let x2 + 4 = t
2x dx = dt
When x = 0; t = 4
When x = 2; t = 22 + 4 = 8
Substituting t and dt in I1
⇒ I1 = [
]
⇒ I1 = 3 [log |8| - log |4|] = 3 log 8/4
⇒ I1 = 3 log � = -3 log 2
I2 = =
[
]
⇒ I2 =
⇒ I2 = = 3π/8
Now I = I1 + I2
I = 3 log � + 3π/8
∴ = 3 log � + 3π/8
Question 20.
Evaluate
Answer:
Let I =
⇒ I =
I = I1 + I2
I1 =
⇒ I1 = [
]
⇒ I1 =
⇒ I1 = e – e – 0 + 1
⇒ I1 = 1
I2 = [
]
⇒ I2 =
⇒ I2 = =
Since, I = I1 + I2
∴ I = 1 +
∴ = 1 +
Question 21.
equals
A. π/3
B. 2π/3
C. π/6
D. π/12
Answer:
Let I =
⇒ I =
⇒ I = [
]
⇒ I = π/12
∴ π/12
Question 22.
equals
A. π/6
B. π/12
C. π/24
D. π/4
Answer:
Let I =
⇒ I =
Taking 9 common from Denominator in I
⇒ I = [
]
⇒ I =
⇒ I =
⇒ I = = π/24
∴ = π/24