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If int(e)^(x) t f(t)dt=sin x-x cos x-(x^...

If `int_(e)^(x) t f(t)dt=sin x-x cos x-(x^(2))/(2)` for all `x in R-{0}`, then the value of `f((pi)/(6))` will be equal to

A

0

B

1

C

`-(1)/(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`overset(x)underset(e )int t f (t) dt =sin x-x cos x -(x^(2))/(2)`
Differentaiting both sides w.r. to x, we get
x f(x)=cos x -cos x +x sin x-x
`f(x)=sin x-1 rArr f((pi)/(6))=(1)/(2)-1=-(1)/(2)`
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