17.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{9f1194cd-cc8a-4f8d-8010-c62fea344c4e-11_536_1214_1340_242}
\end{figure}
Figure 2 shows the line with equation \(y = x + 1\) and the curve with equation \(y = 6 x - x ^ { 2 } - 3\).
The line and the curve intersect at the points \(A\) and \(B\), and \(O\) is the origin.
- Calculate the coordinates of \(A\) and the coordinates of \(B\).
The shaded region \(R\) is bounded by the line and the curve.
- Calculate the area of \(R\).