5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5739a9ae-d1ed-4c9d-a912-587ece5e9627-08_732_780_139_621}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of the curve with parametric equations
$$x = 3 \cos 2 t , \quad y = 2 \tan t , \quad 0 \leq t \leq \frac { \pi } { 4 } .$$
The region \(R\), shown shaded in Figure 5, is bounded by the curve, the \(x\)-axis and the \(y\)-axis.
- Show that the area of \(R\) is given
$$\int _ { 0 } ^ { \frac { \pi } { 4 } } 24 \sin ^ { 2 } t \mathrm {~d} t$$
- Hence, using algebraic integration, find the exact area of \(R\).