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

Options

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

Answer

D

Explanation

Here , `int_(0)^(t^(2)){xf(x)}dx=(2)/(5)t^(2)`
On differentiating both sides , w.r.t.t we get
`t^(2){f(t^(2))}*{(d)/(dt)(t^(2))}-0*f(0){(d)/(dt)(0)}` [ Using Newton Leibnitz 's formula]
`rArrt^(2)f(t^(2))*2t=(4)/(5)t`
`rArrf(t^(2))*=(2)/(5t^(2))`
Now `f((4)/(25))=(2)/(5)*((5)/(2))^(2) " " [ "Putting"t=+-(2)/(5)]`
`=(5)/(2)`