4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4d4aa72e-d781-409d-8401-ccb4241bb12f-06_588_886_255_513}
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\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation \(y = 2 \sin x + \operatorname { cosec } x , 0 < x < \pi\).
The shaded region bounded by the curve, the \(x\)-axis and the lines \(x = \frac { \pi } { 6 }\) and \(x = \frac { \pi } { 2 }\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
Show that the volume of the solid formed is \(\frac { 1 } { 2 } \pi ( 4 \pi + 3 \sqrt { 3 } )\).
4. continued