14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f9ace43-747b-419f-a9d1-d30165d77379-46_812_1091_292_429}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of part of the line \(l\) with equation \(y = 8 - x\) and part of the curve \(C\) with equation \(y = 14 + 3 x - 2 x ^ { 2 }\)
The line \(l\) and the curve \(C\) intersect at the point \(A\) and the point \(B\) as shown.
- Use algebra to find the coordinates of \(A\) and the coordinates of \(B\).
The region \(R\), shown shaded in Figure 5, is bounded by the coordinate axes, the line \(l\), and the curve \(C\).
- Use algebraic integration to calculate the exact area of \(R\).