7.
\begin{figure}[h]
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{13c5a854-baea-4875-82bc-86a19c3be09c-10_691_995_267_477}
\end{figure}
In Figure 2 the curve \(C\) has equation \(y = 6 x - x ^ { 2 }\) and the line \(L\) has equation \(y = 2 x\).
- Show that the curve \(C\) intersects the \(x\)-axis at \(x = 0\) and \(x = 6\).
- Show that the line \(L\) intersects the curve \(C\) at the points \(( 0,0 )\) and \(( 4,8 )\).
The region \(R\), bounded by the curve \(C\) and the line \(L\), is shown shaded in Figure 2.
- Use calculus to find the area of \(R\).