The diagram shows the graph of \(y = e^{\cos x} \sin^3 x\) for \(0 \leq x \leq \pi\), and its maximum point \(M\). The shaded region \(R\) is bounded by the curve and the \(x\)-axis.

1. Find the \(x\)-coordinate of \(M\). Show all necessary working and give your answer correct to 2 decimal places.
2. By first using the substitution \(u = \cos x\), find the exact value of the area of \(R\).