3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ede204ac-09c3-486b-8877-df935e6ed015-06_709_1052_287_552}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { f } ( x )\)
The table below shows corresponding values of \(x\) and \(y\) for this curve between \(x = 0.5\) and \(x = 0.9\)
The values of \(y\) are given to 4 significant figures.
| \(x\) | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 |
| \(y\) | 1.632 | 1.711 | 1.786 | 1.859 | 1.930 |
- Use the trapezium rule, with all the values of \(y\) in the table, to find an estimate for
$$\int _ { 0.5 } ^ { 0.9 } \mathrm { f } ( x ) \mathrm { d } x$$
Give your answer to 3 significant figures.
- Using your answer to part (a), deduce an estimate for
$$\int _ { 0.5 } ^ { 0.9 } ( 3 \mathrm { f } ( x ) + 2 ) \mathrm { d } x$$