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The diagram shows the curve \(y = \sin x \cos 2 x\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\), and its maximum point \(M\).
- Find the \(x\)-coordinate of \(M\), giving your answer correct to 3 significant figures.
- Using the substitution \(u = \cos x\), find the area of the shaded region enclosed by the curve and the \(x\)-axis in the first quadrant, giving your answer in a simplified exact form.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.