16.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{48f9a252-61a2-491d-94d0-8470aee96942-24_771_1484_248_429}
\captionsetup{labelformat=empty}
\caption{Figure 8}
\end{figure}
Figure 8 shows a sketch of the curve with parametric equations
$$x = 4 \cos t \quad y = 2 \sin 2 t \quad 0 \leq t \leq \frac { \pi } { 2 }$$
where \(t\) is a parameter.
The finite region \(R\) is enclosed by the curve \(C\), the \(x\)-axis and the line \(x = 2\), as shown in Figure 7.
a. Show that the area of \(R\) is given by
$$\int _ { \frac { \pi } { 3 } } ^ { \frac { \pi } { 2 } } 16 \sin ^ { 2 } t \cos t \mathrm {~d} t$$
b. Hence, using algebraic integration, find the exact area of \(R\), giving in the form \(a + b \sqrt { 3 }\), where \(a\) and \(b\) are constants to be determined.