11.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1528bec3-7a7a-42c5-bac2-756ff3493818-22_337_892_278_639}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The straight line with equation \(y = x + 4\) cuts the curve with equation \(y = - x ^ { 2 } + 2 x + 24\) at the points \(A\) and \(B\), as shown in Figure 2.
- Use algebra to find the coordinates of the points \(A\) and \(B\).
The finite region \(R\) is bounded by the straight line and the curve and is shown shaded in Figure 2.
- Use calculus to find the exact area of \(R\).