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If int0^(a) f(x) dx = int0^(a) f(a-x) dx...

If `int_0^(a) f(x) dx = int_0^(a) f(a-x) dx`, then the value of `int_0^(pi) x. f(sin x) dx =`

A

`int_0^(pi) x f(cos x) dx`

B

`pi/2 int_0^(pi) f(sin x) dx`

C

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

D

`2/pi int_0^(pi) f(sin x) dx`

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int(-1)^(1) d/(dx) ((tan^(-1)) 1/x) dx =

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  2. If I(n) = int0^(1) x^(n).e^(-x) dx, AA n in N then I(7)-7I(6) =

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  3. If int0^(a) f(x) dx = int0^(a) f(a-x) dx, then the value of int0^(pi) ...

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  4. int0^(pi/2) (asinx+bcosx)/(sinx+cosx) dx =

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  5. The value of int0^(pi/2) 2^(sinx)/(2^(sinx)+2^(cosx)) dx is

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  6. Evaluate the integrals by using substitution int(0)^(1)sin^(-1)((2x)...

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  7. Evaulate int(0)^(pi//4)log(1+tanx)dx.

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  8. If I(1) = inte^(e^(2)) (dx)/(log x) and I(2) = int1^(2) (e^(x)dx)/(x) ...

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  9. If f(x) is integrable on [0,a], then int0^(a) (f(x))/(f(x)+ f(a-x)) dx...

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  10. If In = int0^(pi//4) tan^n theta d theta, then for any +ve integer n, ...

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  11. The value of int(-1/2)^(1/2) (cosx). log ((1-x)/(1+x)) dx is

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  12. The value of int0^(pi) (dx)/(5+3cosx) is

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  13. int0^(pi) (xdx)/(a^(2) cos^(2) x+ b^(2) sin^(2) x) =

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  14. int0^(2pi) (sinx+|sinx|) dx =

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  15. int0^(oo) (xdx)/((1+x)(1+x^(2))) =

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  16. int0^(pi/8) cos^(3) 4 theta d theta =

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  17. int(pi/4)^(pi/2) cosec^(2)x dx =

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  18. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

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  19. If f (x) is defined [-2, 2] by f(x)=4x^(2)-3x+1 and g(x)=(f(-x)-f(x))...

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  20. If k int (0)^(1)x.f(3x)dx = int(0)^(3) t. f(t)dt, then the value of k ...

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