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The value of the integral overset(pi)und...

The value of the integral `overset(pi)underset(0)int log(1+cos x)dx` is

A

`(pi)/(2)log2`

B

`-pi log2`

C

`pi log2`

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
  1. If int(0)^(oo) (log(1+x^(2)))/(1+x^(2))dx=kint(0)^(oo) (log(1+x))/(1+x...

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  2. If int(log2)^(x) (1)/(sqrt(e^(x)-1))dx=(pi)/(6)then x is equal to

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  3. The value of the integral overset(pi)underset(0)int log(1+cos x)dx is

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  4. The integral int(0)^(pi) (1)/(a^(2)-2 a cos x+1)dx (a lt 1) is

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  5. The integral int(0)^(pi//2) f(sin 2 x)sin x dx is equal to

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  6. int(0)^(pi) k(pix-x^(2))^(100)sin2x" dx" is equal to

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  7. The value of the integral int(2)^(4) (sqrt(x^(2)-4))/(x^(4))dx is

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  8. The value of the integral int(0)^(pi)(1)/(a^(2)-2a cos x+1)dx (a gt1),...

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  9. If f(x) and g(x) are continuous functions satisfying (x)=f(a-x) and g(...

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  10. int0^(pi//2) x(sqrt(tan x)+sqrt(cot x))dx equals

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  11. The value of the integral int(1//3)^(1)((x-x^(3))^(1//3))/(x^(4))dx ...

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  12. The value of the integral int(0)^(100pi) sqrt(1-cos2x)" d"xis

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  13. The value of the integral int(-1//2)^(1//2) {((x+1)/(x-1))^(2)+((x-...

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  14. The value of the integral int(1//e)^(e) |logx|dx, is

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  15. The value of int(0)^(pi//2) (sin 8x log cot x)/(cos 2x)dx, is

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  16. The value of int(0)^(pi//2) x^(10) sin x" dx", is then the value of m...

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  17. The value of int(0)^(pi//2) (1)/(1+tan^(3)x)dx is

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  18. The value of int0^pi(sin(n+1/2)x)/(sin(x/2)dx is

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  19. If (d)/(dx)f(x)=g(x) for a le x le b then, int(a)^(b) f(x) g(x) dx eq...

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  20. For any integer n,the integral int(0)^(3) e^(sin^(2)x)cos^(3)(2n+1)x" ...

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