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If f(x) is differentiable and int0^(t^2)...

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
We have,
`overset(t^(2))underset(0)int xf(x)dx=(2)/(5)t^(5)`
`rArr (d)/(dt)overset(t^(2))underset(0)int xf(x)dx=(d)/(dt)((2)/(5)t^(5))`
`rArr 2txxt^(2)f(t^(2))=2t^(4) " "`[USing Leibnitz's rule]
`rArr f(t^(2))=t rArr((4)/(25))=(2)/(5)`
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