7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ee9a9df3-f7a4-41d0-bf8b-e44340c401d6-13_458_933_251_504}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the two curves given by the polar equations
$$\begin{array} { l l }
r = \sqrt { 3 } \sin \theta , & 0 \leqslant \theta \leqslant \pi
r = 1 + \cos \theta , & 0 \leqslant \theta \leqslant \pi
\end{array}$$
- Verify that the curves intersect at the point \(P\) with polar coordinates \(\left( \frac { 3 } { 2 } , \frac { \pi } { 3 } \right)\).
The region \(R\), bounded by the two curves, is shown shaded in Figure 1.
- Use calculus to find the exact area of \(R\), giving your answer in the form \(a ( \pi - \sqrt { 3 } )\), where \(a\) is a constant to be found.