9709 P33 - Jun 2014 - Q9
1795
The diagram shows the curve \(y = e^{2\sin x} \cos x\) for \(0 \leq x \leq \frac{1}{2}\pi\), and its maximum point \(M\).
(i) Using the substitution \(u = \sin x\), find the exact value of the area of the shaded region bounded by the curve and the axes.
(ii) Find the \(x\)-coordinate of \(M\), giving your answer correct to 3 decimal places.
