Answer
$\frac{1}{2}sinh1$
Work Step by Step
average value is
= $\frac{1}{1-0}\int_0^{2}xcosh(x^{2})dx$
let
$u$ = $x^{2}$
$du$ = $2xdx$
so
$\frac{1}{1-0}\int_0^{2}xcosh(x^{2})dx$ = $\frac{1}{2}\int_0^{1}coshudu$ = $\frac{1}{2}sinhu|_0^1$ = $\frac{1}{2}sinh1$
