6
\includegraphics[max width=\textwidth, alt={}, center]{3b217eb4-3bd3-4800-a913-749754bf109f-3_401_586_817_778}
The diagram shows part of the curve with equation
$$y = 4 \sin ^ { 2 } x + 8 \sin x + 3$$
and its point of intersection \(P\) with the \(x\)-axis.
- Find the exact \(x\)-coordinate of \(P\).
- Show that the equation of the curve can be written
$$y = 5 + 8 \sin x - 2 \cos 2 x$$
and use integration to find the exact area of the shaded region enclosed by the curve and the axes.