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If f(x)=f(a+b-x) for all `x in[a,b]` and `int_(a)^(b) xf(x) dx=k int_(a)^(b) f(x) dx`, then the value of k, is

A

`(a+b)/(2)`

B

`(a-b)/(2)`

C

`(a^(2)+b^(2))/(2)`

D

`(a^(2)-b^(2))/(2)`

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Exercise
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  10. If I=int(0)^(1//2) (1)/(sqrt(1-x^(2n)))dxthen which one of the follow...

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  11. If I=int(0)^(1//2) (sin^(2)n x)/(sin^(2)x)dxthen which one of the foll...

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  13. The value of the integral int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal...

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

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

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

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