9. \(y\)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f31b6f1-33b5-4bca-9030-cf93760b454d-13_895_1308_207_294}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The finite region \(R\), as shown in Figure 2, is bounded by the \(x\)-axis and the curve with equation
$$y = 27 - 2 x - 9 \sqrt { } x - \frac { 16 } { x ^ { 2 } } , \quad x > 0$$
The curve crosses the \(x\)-axis at the points \(( 1,0 )\) and \(( 4,0 )\).
- Complete the table below, by giving your values of \(y\) to 3 decimal places.
| \(x\) | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 |
| \(y\) | 0 | 5.866 | | 5.210 | | 1.856 | 0 |
- Use the trapezium rule with all the values in the completed table to find an approximate value for the area of \(R\), giving your answer to 2 decimal places.
- Use integration to find the exact value for the area of \(R\).