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`

Question

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`

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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29