15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{75d68987-2314-4c8f-8160-24977c5c4e34-40_545_794_294_584}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
The straight line \(l\) with equation \(y = 5 - 3 x\) cuts the curve \(C\), with equation \(y = 20 x - 12 x ^ { 2 }\), at the points \(P\) and \(Q\), as shown in Figure 3.
- Use algebra to find the exact coordinates of the points \(P\) and \(Q\).
The finite region \(R\), shown shaded in Figure 3, is bounded by the line \(l\), the \(x\)-axis and the curve \(C\).
- Use calculus to find the exact area of \(R\).