2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{db4ec300-8081-4d29-acd5-0aae789d8f95-04_398_421_251_765}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the graph of
$$y = 1 - \log _ { 10 } ( \sin x ) \quad 0 < x < \pi$$
where \(x\) is in radians.
The table below shows some values of \(x\) and \(y\) for this graph, with values of \(y\) given to 3 decimal places.
| \(x\) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| \(y\) | 1.319 | | 1.001 | | 1.223 | 1.850 |
- Complete the table above, giving values of \(y\) to 3 decimal places.
- Use the trapezium rule with all the \(y\) values in the completed table to find, to 2 decimal places, an estimate for
$$\int _ { 0.5 } ^ { 3 } \left( 1 - \log _ { 10 } ( \sin x ) \right) \mathrm { d } x$$
- Use your answer to part (b) to find an estimate for
$$\int _ { 0.5 } ^ { 3 } \left( 3 + \log _ { 10 } ( \sin x ) \right) \mathrm { d } x$$