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The value of int0^1 (2^(2x+1)-5^(2x-1))...

The value of `int_0^1 (2^(2x+1)-5^(2x-1))/(10^(x))dx` is

A

`(3)/(5){(2)/(loge((2)/(5)))+(1)/(2loge((5)/(2)))}`

B

`-(3)/(5){(2)/(loge((2)/(5)))+(1)/(2loge((5)/(2)))}`

C

`(3)/(5){(2)/(loge^(((2)/(5))))-(1)/(2loge^(((5)/(2))))}`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. The value of the integral int(0)^(100) sin(x-[x])pidx, is

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  2. The difference between the greatest and least values of the function p...

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  3. The value of int0^1 (2^(2x+1)-5^(2x-1))/(10^(x))dx is

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  4. The value of int(0)^(pi//2) (cos3x+1)/(2 cos x-1) dx is

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  5. The value of int(0)^(16pi//3) |sinx|dx is

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  6. If int(0)^(npi) f(cos^(2)x)dx=k int(0)^(pi) f(cos^(2)x)dx, then the va...

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  7. The value of int(-pi)^(pi) sinx f(cosx)dx is

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  8. If a lt int(0)^(2pi)) (1)/(10+3 cos x)dx lt b. Then the ordered pair (...

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  9. The value of the integral int0^(oo) (x logx)/((1+x^(2)))dxis

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  10. The value of the integral int(-pi//2)^(pi//2) sqrt(cos -cos^(2)x)dx is

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  11. The value of the integral int(-pi//2)^(pi//2) sqrt((1+cos^(2)x)/(2))dx...

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  12. Let I(1)=int(1)^(2)(1)/(sqrt(1+x^(2)))dx and I(2)=int(1)^(2)(1)/(x)dx....

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  13. int(0)^(pi//4) (sin x +cos x)/(3+sin2x)dx is equal to

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  14. The value of the integral int(0)^(pi//4) (sin theta+cos theta)/(9+16 s...

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  15. Let (d)/(dx)(f(x))=(e^(sinx))/(x),x gt 0. "If" int1^(4) (3)/(x)e^(sinx...

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  16. If I=int(-1)^(1) {[x^(2)]+log((2+x)/(2-x))}dx where [x] denotes the gr...

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  17. The value of int(-pi//2)^(pi//2)(x^(2)+x cosx+tan^(5)x+1)dx is equal t...

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  18. If int(-1)^(4) f(x)=4 and int(2)^(7) (3-f(x))dx=7, then the value of i...

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  19. The value of I=int(0)^(pi//2) (1)/(1+cosx)dx is

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  20. int(0)^(pi//2) (sin^(2)x)/(sinx+cosx)dxis equal to

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