14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e878227b-d625-4ef2-ac49-a9dc05c5321a-36_652_791_223_548}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Diagram NOT drawn to scale
Figure 2 shows part of the line \(l\) with equation \(y = 2 x - 3\) and part of the curve \(C\) with equation \(y = x ^ { 2 } - 2 x - 15\)
The line \(l\) and the curve \(C\) intersect at the points \(A\) and \(B\) as shown.
- Use algebra to find the coordinates of \(A\) and the coordinates of \(B\).
In Figure 2, the shaded region \(R\) is bounded by the line \(l\), the curve \(C\) and the positive \(x\)-axis.
- Use integration to calculate an exact value for the area of \(R\).