15.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{725966d1-d29d-4c9d-b850-c67d55cdd6e8-24_712_972_296_598}
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\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of part of the curve \(y = 2 x + \frac { 8 } { x ^ { 2 } } - 5 , x > 0\).
The point \(A \left( 4 , \frac { 7 } { 2 } \right)\) lies on C . The line \(l\) is the tangent to \(C\) at the point A .
The region \(\boldsymbol { R }\), shown shaded in figure 5 is bounded by the line \(l\), the curve \(C\), the line with equation \(x = 1\) and the \(x\)-axis.
Find the exact area of \(\boldsymbol { R }\).
(Solutions based entirely on graphical or numerical methods are not acceptable.)
(Total for Question 15 is 9 marks)