4 In this question you must show detailed reasoning.
Fig. 4 shows the region bounded by the curve \(y = \sec \frac { 1 } { 2 } x\), the \(x\)-axis, the \(y\)-axis and the line \(x = \frac { 1 } { 2 } \pi\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{01a574f1-f6f6-40f5-baa5-535c36269731-2_501_670_1329_242}
\captionsetup{labelformat=empty}
\caption{Fig. 4}
\end{figure}
This region is rotated through \(2 \pi\) radians about the \(x\)-axis.
Find, in exact form, the volume of the solid of revolution generated.