5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d93ae982-9395-4311-9972-be727b3ce954-14_510_723_269_607}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows the finite region \(R\) which is bounded by part of the curve with equation \(y = \sin x\), the \(x\)-axis and the line with equation \(x = \frac { \pi } { 2 }\). A uniform solid \(S\) is formed by rotating \(R\) through \(2 \pi\) radians about the \(x\)-axis.
Using algebraic integration,
- show that the volume of \(S\) is \(\frac { \pi ^ { 2 } } { 4 }\)
- find, in terms of \(\pi\), the \(x\) coordinate of the centre of mass of \(S\).