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\includegraphics[max width=\textwidth, alt={}, center]{2a3df76c-2323-470c-8586-009753a4c1e3-12_357_565_260_790} The diagram shows the curve \(y = 5 \sin ^ { 2 } x \cos ^ { 3 } x\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\), and its maximum point \(M\). The shaded region \(R\) is bounded by the curve and the \(x\)-axis.

1. Find the \(x\)-coordinate of \(M\), giving your answer correct to 3 decimal places.
2. Using the substitution \(u = \sin x\) and showing all necessary working, find the exact area of \(R\). [4]