1.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ac7d862f-d10d-45ed-9077-ae4c7413cbf6-02_390_675_246_630}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The curve shown in Figure 1 has equation \(y = \mathrm { e } ^ { x } \sqrt { } ( \sin x ) , 0 \leqslant x \leqslant \pi\). The finite region \(R\) bounded by the curve and the \(x\)-axis is shown shaded in Figure 1.
- Complete the table below with the values of \(y\) corresponding to \(x = \frac { \pi } { 4 }\) and \(\frac { \pi } { 2 }\), giving your answers to 5 decimal places.
| \(x\) | 0 | \(\frac { \pi } { 4 }\) | \(\frac { \pi } { 2 }\) | \(\frac { 3 \pi } { 4 }\) | \(\pi\) |
| \(y\) | 0 | | | 8.87207 | 0 |
- Use the trapezium rule, with all the values in the completed table, to obtain an estimate for the area of the region \(R\). Give your answer to 4 decimal places.