7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{216f5735-a7ad-4d70-9da9-ae1f098a97d9-14_620_615_278_662}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
- Find \(\int \mathrm { e } ^ { 2 x } \sin x \mathrm {~d} x\)
Figure 2 shows a sketch of part of the curve with equation
$$y = \mathrm { e } ^ { 2 x } \sin x \quad x \geqslant 0$$
The finite region \(R\) is bounded by the curve and the \(x\)-axis and is shown shaded in Figure 2.
- Show that the exact area of \(R\) is \(\frac { \mathrm { e } ^ { 2 \pi } + 1 } { 5 }\)
(Solutions relying on calculator technology are not acceptable.)
Question 7 continue