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The diagram shows the graph of \(y = \mathrm { e } ^ { \cos x } \sin ^ { 3 } x\) for \(0 \leqslant x \leqslant \pi\), and its maximum point \(M\). The shaded region \(R\) is bounded by the curve and the \(x\)-axis.
- Find the \(x\)-coordinate of \(M\). Show all necessary working and give your answer correct to 2 decimal places.
- By first using the substitution \(u = \cos x\), find the exact value of the area of \(R\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.