6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{7d07e1ad-d87a-4eb5-a15e-05b927892915-14_768_712_212_616}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
The curve shown in Figure 2 has equation
$$y ^ { 2 } = 3 \tan \left( \frac { x } { 2 } \right) , \quad 0 < x < \pi , \quad y > 0$$
The finite region \(R\), shown shaded in Figure 2, is bounded by the curve, the line with equation \(x = \frac { \pi } { 3 }\) the \(x\)-axis and the line with equation \(x = \frac { \pi } { 2 }\)
The region \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis to generate a solid of revolution.
Show that the exact value of the volume of the solid generated may be written as \(A \ln \left( \frac { 3 } { 2 } \right)\), where \(A\) is a constant to be found.