If f(x) is differentibale and $\int_0^{t^2} xf(x)dx =\frac{2}{5}t^5$ then $f(\frac{4}{25})$ equals
Answer & explanation
Correct answer: option 1
$\int_0^{t^2} xf(x)dx =\frac{2}{5}t^5$
differentiate both side w.r.t. t
$t^2\, f(t^2)\, 2t =\frac{10t^4}{5}⇒f(t^2) = t$
put $t = 2/5, f(4/ 25) = 2/5$