\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3b99072a-cd16-4c1d-9e44-085926a3ba24-03_473_654_233_603}
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\caption{Figure 1}
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Figure 1 shows a sketch of part of the graph of \(y = \frac { 12 } { \sqrt { \left( x ^ { 2 } - 2 \right) } } , x \geqslant 2\)
The table below gives values of \(y\) rounded to 3 decimal places.
| \(x\) | 2 | 5 | 8 | 11 |
| \(y\) | 8.485 | 2.502 | 1.524 | 1.100 |
- Use the trapezium rule with all the values of \(y\) from the table to find an approximate value, to 2 decimal places, for
$$\int _ { 2 } ^ { 11 } \frac { 12 } { \sqrt { \left( x ^ { 2 } - 2 \right) } } \mathrm { d } x$$
- Use your answer to part (a) to estimate a value for
$$\int _ { 2 } ^ { 11 } \left( 1 + \frac { 6 } { \sqrt { \left( x ^ { 2 } - 2 \right) } } \right) d x$$