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The diagram shows the curve \(y = \sin ^ { 3 } x \sqrt { } ( \cos x )\) for \(0 \leqslant x \leqslant \frac { 1 } { 2 } \pi\), and its maximum point \(M\).
- Using the substitution \(u = \cos x\), find by integration the exact area of the shaded region bounded by the curve and the \(x\)-axis.
- Showing all your working, find the \(x\)-coordinate of \(M\), giving your answer correct to 3 decimal places.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.