4.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{9bf05d7e-7bb9-40f6-b626-69a8a6eda5a5-05_556_723_299_632}
\end{figure}
Figure 1 shows the finite shaded region, \(R\), which is bounded by the curve \(y = x \mathrm { e } ^ { x }\), the line \(x = 1\), the line \(x = 3\) and the \(x\)-axis.
The region \(R\) is rotated through 360 degrees about the \(x\)-axis.
Use integration by parts to find an exact value for the volume of the solid generated.
(8)