6.
$$y = \frac { 5 } { 3 x ^ { 2 } - 2 }$$
- Complete the table below, giving the values of \(y\) to 2 decimal places.
| \(x\) | 2 | 2.25 | 2.5 | 2.75 | 3 |
| \(y\) | 0.5 | 0.38 | | | 0.2 |
- Use the trapezium rule, with all the values of \(y\) from your table, to find an approximate value for \(\int _ { 2 } ^ { 3 } \frac { 5 } { 3 x ^ { 2 } - 2 } \mathrm {~d} x\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{be8f9187-055a-476f-974d-22e8e16e9996-08_537_743_941_603}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation \(y = \frac { 5 } { 3 x ^ { 2 } - 2 } , x > 1\).
At the points \(A\) and \(B\) on the curve, \(x = 2\) and \(x = 3\) respectively.
The region \(S\) is bounded by the curve, the straight line through \(B\) and ( 2,0 ), and the line through \(A\) parallel to the \(y\)-axis. The region \(S\) is shown shaded in Figure 2. - Use your answer to part (b) to find an approximate value for the area of \(S\).