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 \(b\).