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

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`

A

`(2)/(5)`

B

`-(5)/(2)`

C

1

D

`(5)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Here , `int_(0)^(t^(2))x f (x) dx = (2)/(5)t^(5)` Using Newton Leibnitz 's formula , differentiating both sides , we get
`t^(2){f(t^(2))} {(d)/(dt)(t^(2))}-0*f(0){(d)/(dt)(0)}=2t^(4)`
`rArr t^(2)f(t^(2))2 t = 2t^(4)rArrf(t^(2))=t`
`:. f((4)/(25))=-(2)/(5)` [ Putting ` t= (2)/(5)]`
`rArrf ((4)/(25))=(2)/(5)`
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