5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{b71c9832-e502-4a25-85fb-a49c03ea9209-08_663_899_146_495}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve with equation \(y = \frac { 1 } { \sqrt { 3 x + 1 } }\).
The shaded region is bounded by the curve, the \(x\)-axis and the lines \(x = 1\) and \(x = 5\).
- Find the area of the shaded region.
The shaded region is rotated completely about the \(x\)-axis.
- Find the volume of the solid formed, giving your answer in the form \(k \pi \ln 2\), where \(k\) is a simplified fraction.
5. continued