If f(x) is differentiable and ∫0t2 xf(x)dx=25t5, then f425 equals

# If $f\left(x\right)$ is differentiable and ${\int }_{0}^{{t}^{2}} xf\left(x\right)dx=\frac{2}{5}{t}^{5},$ then $f\left(\frac{4}{25}\right)$ equals

1. A

$2/5$

2. B

$-5/2$

3. C

1

4. D

$5/2$

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### Solution:

We have,

[Using Leibnitz's rule]

$⇒f\left({t}^{2}\right)=t⇒f\left(\frac{4}{25}\right)=\frac{2}{5}$

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