Edexcel C4 2008 January — Question 3

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2008
SessionJanuary
TopicVolumes of Revolution

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ac7d862f-d10d-45ed-9077-ae4c7413cbf6-04_493_490_278_712} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The curve shown in Figure 2 has equation \(y = \frac { 1 } { ( 2 x + 1 ) }\). The finite region bounded by the curve, the \(x\)-axis and the lines \(x = a\) and \(x = b\) is shown shaded in Figure 2. This region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis to generate a solid of revolution. Find the volume of the solid generated. Express your answer as a single simplified fraction, in terms of \(a\) and \(b\).