SPS SPS SM Pure 2024 September — Question 13

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionSeptember
TopicStandard Integrals and Reverse Chain Rule

13. In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b616e3c-db87-430e-91c1-63a24e2f9593-28_633_725_475_676} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a sketch of the curve with equation $$y = \frac { 1 } { 2 } x ^ { 2 } + \frac { 1458 } { \sqrt { x ^ { 3 } } } - 74 \quad x > 0$$ The point \(P\) is the only stationary point on the curve.
The line \(l\) passes through the point \(P\) and is parallel to the \(x\)-axis.
The region \(R\), shown shaded in Figure 2, is bounded by the curve, the line \(l\) and the line with equation \(x = 4\) Use algebraic integration to find the exact area of \(R\).
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