7.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{1425d933-47e3-4a12-bcab-fd2ca41827e2-3_531_1216_998_189}
\end{figure}
Fig. 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 \(R\).