8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c46ca445-cf59-4664-931e-add9f2f81851-26_582_773_255_648}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
\section*{In this question you must show all stages of your working.}
\section*{Solutions relying entirely on calculator technology are not acceptable.}
A curve \(C\) has parametric equations
$$x = \sin ^ { 2 } t \quad y = 2 \tan t \quad 0 \leqslant t < \frac { \pi } { 2 }$$
The point \(P\) with parameter \(t = \frac { \pi } { 4 }\) lies on \(C\).
The line \(l\) is the normal to \(C\) at \(P\), as shown in Figure 3.
- Show, using calculus, that an equation for \(l\) is
$$8 y + 2 x = 17$$
The region \(S\), shown shaded in Figure 3, is bounded by \(C , l\) and the \(x\)-axis.
- Find, using calculus, the exact area of \(S\).