If f(x) is differentiable and `int_(0)^(t^(2)) x f(x) dx=(2)/(5)t^(5)`, then f`f((4)/(25))` equals

Options

A. `2//5`
B. `-5//2`
C. 1
D. `5//2`

Answer

A

Explanation

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)`