Find the Average Value of the Function $f(t)=8 t \sin t^{2}$

Multiple Choice

Find the average value of the function $f(t) =8 t \sin t^{2}$ on the interval $[0, \sqrt{\pi}]$ .

A) $\frac{16}{\pi}$
B) $\frac{8}{\pi}$
C) $\frac{8}{\sqrt{\pi}}$
D) $\frac{1}{\pi}$
E) $\frac{16}{\sqrt{\pi}}$