6.
\includegraphics[max width=\textwidth, alt={}, center]{0214eebf-93f2-4338-9222-443000115225-4_346_1040_303_548} \section*{Figure 1} Figure 1 shows a sketch of the curve \(C _ { 1 }\) with equation $$y = \cos ( \cos x ) \sin x \quad \text { for } \quad 0 \leqslant x \leqslant \pi$$ （a）Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\)
（b）Hence verify that the turning point is at \(x = \frac { \pi } { 2 }\) and find the \(y\) coordinate of this point．
（c）Find the area of the region bounded by \(C _ { 1 }\) and the positive \(x\)－axis between \(x = 0\) and \(x = \pi\) Figure 2 shows a sketch of the curve \(C _ { 1 }\) and the curve \(C _ { 2 }\) with equation $$y = \sin ( \cos x ) \sin x \quad \text { for } \quad 0 \leqslant x \leqslant \pi$$ \begin{figure}[h] \end{figure} The curves \(C _ { 1 }\) and \(C _ { 2 }\) intersect at the origin and the point \(A ( a , b )\) ，where \(a < \pi\)
（d）Find \(a\) and \(b\) ，giving \(b\) in a form not involving trigonometric functions．
（e）Find the area of the shaded region between \(C _ { 1 }\) and \(C _ { 2 }\)