6.

$$y = \frac { 5 } { 3 x ^ { 2 } - 2 }$$
\begin{enumerate}[label=(\alph*)]
\item Complete the table below, giving the values of $y$ to 2 decimal places.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 2 & 2.25 & 2.5 & 2.75 & 3 \\
\hline
$y$ & 0.5 & 0.38 &  &  & 0.2 \\
\hline
\end{tabular}
\end{center}
\item 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]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{be8f9187-055a-476f-974d-22e8e16e9996-08_537_743_941_603}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\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.
\item Use your answer to part (b) to find an approximate value for the area of $S$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2 2011 Q6 [9]}}