Edexcel C4 2013 January — Question 6

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2013
SessionJanuary
TopicIndefinite & Definite Integrals

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a98d4a7f-1e6d-4294-9b5c-c945e8fbe83e-09_862_1534_219_205} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a sketch of part of the curve with equation \(y = 1 - 2 \cos x\), where \(x\) is measured in radians. The curve crosses the \(x\)-axis at the point \(A\) and at the point \(B\).
  1. Find, in terms of \(\pi\), the \(x\) coordinate of the point \(A\) and the \(x\) coordinate of the point \(B\). The finite region \(S\) enclosed by the curve and the \(x\)-axis is shown shaded in Figure 3. The region \(S\) is rotated through \(2 \pi\) radians about the \(x\)-axis.
  2. Find, by integration, the exact value of the volume of the solid generated.