5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{cd449136-cb09-49eb-8812-c863c0e7bd4e-10_506_728_267_632}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curves given by the polar equations
$$r = 2 , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }$$
and \(\quad r = 1.5 + \sin 3 \theta , \quad 0 \leqslant \theta \leqslant \frac { \pi } { 2 }\).
- Find the coordinates of the points where the curves intersect.
The region \(S\), between the curves, for which \(r > 2\) and for which \(r < ( 1.5 + \sin 3 \theta )\), is shown shaded in Figure 1.
- Find, by integration, the area of the shaded region \(S\), giving your answer in the form \(a \pi + b \sqrt { 3 }\), where \(a\) and \(b\) are simplified fractions.
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