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int0^(pi) x f (sin x) dx is equal to :...

`int_0^(pi) x f (sin x) dx` is equal to :

A

`pi int_0^(pi) f(cosx) dx`

B

`pi int_0^(pi) f(sinx) dx`

C

`pi/2 int_0^(pi) f(sinx) dx`

D

`pi int_0^(pi/2) f(cosx) dx`

Text Solution

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The correct Answer is:
D
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  2. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

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  3. int0^(pi) x f (sin x) dx is equal to :

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  4. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

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  5. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

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  6. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

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  7. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

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  8. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

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  9. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

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  10. Let f(x) = int1^x sqrt(2 - t^2) dt. Then the real roots of the equatio...

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  11. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

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  12. If I(m,n) = int0^1 t^m (1 + t)^n dt , m, n in R, then I(m, n) is :

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  13. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

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  14. If f(x) is differentiable and int0^(t^2) x f(x) dx = 2/5 t^5, then f (...

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  15. If int(sin x)^(1) t^2 f(t) dt = 1 - sin x, then the value of f(1/(sqrt...

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  16. int(-2)^(0) {x^3 + 3x^2 + 3x + 3 + (x + 1) cos (x + 1)} dx is equal to...

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  17. int0^(pi//2)(dx)/(1 + tanx)=

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  18. I(m,n) = int0^1 x^m (ln x)^n dx equals:

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  19. int0^(1) sqrt(x(1-x)) dx=

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  20. Evaluate int(0)^(pi)(xsinx)/(1+cos^(2)x)dx

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