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If `f(x)` is differentiable and `int_0^(t^2) x f(x) dx=2/5t^5,` then `f(4/(25))` equals (a)`2/5` (b) `-5/2` (c)`1` (d) `5/2`

A

`2//5`

B

`-5//2`

C

`1`

D

`5//2`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(t^(2)) xf(x)dx=2/5t^(5)` (Here `t gt0`)
Differentiating bothsides w.r.t `t` we get
`t^(2)f(t^(2))xx2t=2/5xx5t^(4)`
or `f(t^(2))=t`
Put `t=2/5`. Then `f(4/25)=2/5`
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