SPS SPS SM 2020 June — Question 13

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2020
SessionJune
TopicArea Under & Between Curves

13. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2033889-3cc5-48de-9bdb-cb1861921a2a-12_803_981_301_651} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} Figure 5 shows a sketch of the curve \(C\) with equation \(y = ( x - 2 ) ^ { 2 } ( x + 3 )\)
The region \(R\), shown shaded in Figure 5, is bounded by \(C\), the vertical line passing through the maximum turning point of \(C\) and the \(x\)-axis. Find the exact area of \(R\).
(Solutions based entirely on graphical or numerical methods are not acceptable.)