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The value of the integral int(0)^(pi//4)...

The value of the integral `int_(0)^(pi//4) (sin theta+cos theta)/(9+16 sin 2theta)d theta`, is

A

log 3

B

log 2

C

`(1)/(20)log3`

D

`(1)/(20)log2`

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. 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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  2. int(0)^(pi//4) (sin x +cos x)/(3+sin2x)dx is equal to

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

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

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

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

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

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

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  10. The value of the integral int(a)^(b) (|x|)/(x)dx, a lt b is

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  11. The value of the integral int(0)^(2pi)(sin2 theta)/(a-b cos theta)d ...

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  12. The value of the integral int(0)^(1) x(1-x)^(n)dx, is

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  13. The value of the integral int(0)^(3alpha) cosec (x-alpha)cosec(x-2al...

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  14. The value of the integral int(0)^(pi) (sin k x)/(sin x)dx (k is an eve...

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  15. The value of the integral int(0)^(1)(1)/(x^(2)+2x cos alpha+1)dxis equ...

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  16. The greater value of F(x)=int(1)^(x) |t|dt on the interval [-1//2,1//2...

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  17. The value of the integral int(0)^(pi//2) |sin x-cos x|dx, is

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  18. The value of the integral int(0)^(pi//4) sin^(-4)x dx, is

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  19. The value of the integral I=int(1)^(oo) (x^(2)-2)/(x^(3)sqrt(x^(2)-1))...

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  20. int(0)^(1) |sin 2pi x|dx id equal to

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