8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0454f5f6-b5ee-40b1-bc6a-ff8aeb06a455-11_668_1267_292_367}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = 10 + 8 x + x ^ { 2 } - x ^ { 3 }\).
The curve has a maximum turning point \(A\).
- Using calculus, show that the \(x\)-coordinate of \(A\) is 2 .
The region \(R\), shown shaded in Figure 2, is bounded by the curve, the \(y\)-axis and the line from \(O\) to \(A\), where \(O\) is the origin.
- Using calculus, find the exact area of \(R\).