6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42116a65-60ec-4dff-a05e-bab529939e1e-07_611_1326_280_310}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the graph of the curve with equation
$$y = \frac { 16 } { x ^ { 2 } } - \frac { x } { 2 } + 1 , \quad x > 0$$
The finite region \(R\), bounded by the lines \(x = 1\), the \(x\)-axis and the curve, is shown shaded in Figure 1. The curve crosses the \(x\)-axis at the point \(( 4,0 )\).
- Complete the table with the values of \(y\) corresponding to \(x = 2\) and 2.5
| \(x\) | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 |
| \(y\) | 16.5 | 7.361 | | | 1.278 | 0.556 | 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 \(R\).