Given that
\(y=x^{2} \sin x,\)
(i) show that the mean value of \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant \frac{1}{2} \pi\) is \(\frac{1}{2} \pi\),
(ii) find the mean value of \(\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}\) with respect to \(x\) over the interval \(0 \leqslant x \leqslant \frac{1}{2} \pi\).