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If int(0)^(x^(2)(1+x))f(t)dt=x, then the...

If `int_(0)^(x^(2)(1+x))f(t)dt=x`, then the value of f(2) is.

A

`1//2`

B

`1//3`

C

`1//4`

D

`1//5`

Text Solution

Verified by Experts

The correct Answer is:
D
Differentiating both sides w.r.t. x, then
`f(x^(2)(1+x))xx(2x+3x^(2))=1`
At `x=1rArr f(2)=(1)/(5)`
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