2.
\includegraphics[max width=\textwidth, alt={}, center]{b124d427-1f9b-4770-95bb-ed79bae5b4fb-1_460_805_587_486}
The diagram shows the curve with equation \(y = \frac { 1 } { 2 } \ln 3 x\).
- Express the equation of the curve in the form \(x = \mathrm { f } ( y )\).
The shaded region is bounded by the curve, the coordinate axes and the line \(y = 1\).
- Find, in terms of \(\pi\) and e, the volume of the solid formed when the shaded region is rotated through four right angles about the \(y\)-axis.