4. The finite region \(R\) is bounded by the curve with equation \(y = \frac { 1 } { 2 x - 1 }\), the \(x\)-axis and the lines \(x = 1\) and \(x = 2\).
- Find the exact area of \(R\).
- Show that the volume of the solid formed when \(R\) is rotated through four right angles about the \(x\)-axis is \(\frac { 1 } { 3 } \pi\).