9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{423eb549-0873-4185-8faf-12dedafcd108-13_849_841_214_571}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve with equation \(y = \mathrm { e } ^ { \sqrt { x } } , x > 0\)
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines \(x = 4\) and \(x = 9\)
- Use the trapezium rule, with 5 strips of equal width, to obtain an estimate for the area of \(R\), giving your answer to 2 decimal places.
- Use the substitution \(u = \sqrt { x }\) to find, by integrating, the exact value for the area of \(R\).