2
\includegraphics[max width=\textwidth, alt={}, center]{8c358a10-a3e1-47b5-ae62-30ba6b76c167-2_627_551_429_790} The diagram shows part of the curve \(y = \left( x ^ { 3 } + 1 \right) ^ { \frac { 1 } { 2 } }\) and the point \(P ( 2,3 )\) lying on the curve. Find, showing all necessary working, the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.