Edexcel C4 2006 June — Question 3

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2006
SessionJune
TopicVolumes of Revolution

3. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{c0c6303b-f527-4e68-91bc-5c9c6ffa8de8-04_423_777_306_569}
\end{figure} The curve with equation \(y = 3 \sin \frac { x } { 2 } , 0 \leqslant x \leqslant 2 \pi\), is shown in Figure 1. The finite region enclosed by the curve and the \(x\)-axis is shaded.
  1. Find, by integration, the area of the shaded region. This region is rotated through \(2 \pi\) radians about the \(x\)-axis.
  2. Find the volume of the solid generated.