3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c46ca445-cf59-4664-931e-add9f2f81851-08_419_665_255_708}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
\section*{In this question you must show all stages of your working.}
\section*{Solutions relying entirely on calculator technology are not acceptable.}
Figure 1 shows a sketch of the curve with equation
$$y = \sqrt { \frac { 3 x } { 3 x ^ { 2 } + 5 } } \quad x \geqslant 0$$
The finite region \(R\), shown shaded in Figure 1, is bounded by the curve, the \(x\)-axis and the lines with equations \(x = \sqrt { 5 }\) and \(x = 5\)
The region \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
Use integration to find the exact volume of the solid generated. Give your answer in the form \(a \ln b\), where \(a\) is an irrational number and \(b\) is a prime number.