1.
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\caption{Figure 1}
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The region \(R\), shown shaded in Figure 1, is bounded by the curve with equation \(y = \frac { 1 } { x }\), the line with equation \(x = 1\), the positive \(x\)-axis and the line with equation \(x = a\) where \(a > 1\) A uniform solid \(S\) is formed by rotating \(R\) through \(2 \pi\) radians about the \(x\)-axis.
- Show that the volume of \(S\) is
$$\pi \left( 1 - \frac { 1 } { a } \right)$$
- Find the \(x\) coordinate of the centre of mass of \(S\).