Edexcel P4 2021 January — Question 7

Exam BoardEdexcel
ModuleP4 (Pure Mathematics 4)
Year2021
SessionJanuary
TopicIntegration by Parts

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}
  1. 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.
  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