13. In this question you must show detailed reasoning.
The diagram below shows the curve \(r = \sqrt { \sin \theta } \mathrm { e } ^ { \frac { 1 } { 3 } \cos \theta }\) for \(0 \leqslant \theta \leqslant \pi\).
\includegraphics[max width=\textwidth, alt={}, center]{0d8a4ccd-f88a-4f03-a70f-61864d2e30e2-26_686_1061_317_539}
- Find the exact area enclosed by the curve.
- Show that the greatest value of \(r\) on the curve is \(\sqrt { \frac { \sqrt { 3 } } { 2 } } \mathrm { e } ^ { \frac { 1 } { 6 } }\).
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