9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a377da06-a968-438c-bec2-ae55283dae47-28_533_1095_258_365}
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\caption{Figure 2}
\end{figure}
Diagram not drawn to scale
- Find
$$\int \frac { 1 } { ( 2 x - 1 ) ^ { 2 } } d x$$
Figure 2 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\) where
$$f ( x ) = \frac { 12 } { ( 2 x - 1 ) } \quad 1 \leqslant x \leqslant 5$$
The finite region \(R\), shown shaded in Figure 2, is bounded by the line with equation \(x = 1\), the curve with equation \(y = \mathrm { f } ( x )\) and the line with equation \(y = \frac { 4 } { 3 }\).
The region \(R\) is rotated through \(2 \pi\) radians about the \(x\)-axis to form a solid of revolution.
- Find the exact value of the volume of the solid generated, giving your answer in its simplest form.
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