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If f:R rarr (0,oo)be a differentiable f...

If `f:R rarr (0,oo)`be a differentiable function `f(x)` satisfying
`f(x+y)-f(x-y)=f(x)*{f(y)-f(y)-y}, AA x, y in R, (f(y)!= f(-y) " for all " y in R)` and `f'(0)=2010`.
Now, answer the following questions.
let `g(x)=log_(e)(sin x)`, and `int f(g(x))cos x dx=h(x)+c`, (where c is constant of integration), then `h(pi/2)` is equal to

A

0

B

`(1)/(2010)`

C

1

D

`(1)/(2011)`

Text Solution

Verified by Experts

The correct Answer is:
D
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