Edexcel C4 2012 January — Question 4

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
Year2012
SessionJanuary
TopicVolumes of Revolution

4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8c963567-d751-4898-b7a7-7095d90514f0-06_606_1185_237_383} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the curve with equation $$y = \sqrt { } \left( \frac { 2 x } { 3 x ^ { 2 } + 4 } \right) , x \geqslant 0$$ The finite region \(S\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the line \(x = 2\) The region \(S\) is rotated \(360 ^ { \circ }\) about the \(x\)-axis.
Use integration to find the exact value of the volume of the solid generated, giving your answer in the form \(k \ln a\), where \(k\) and \(a\) are constants.