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}
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\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 \(R\).
(8)
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