- In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
\begin{figure}[h]
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\caption{Figure 2}
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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.
- Use calculus to show that the \(x\) coordinate of \(P\) is 9
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 \(R\).