\end{figure}
In Fig. 1, the curve \(C\) has equation \(y = \mathrm { f } ( x )\), where
$$\mathrm { f } ( x ) = x + \frac { 2 } { x ^ { 2 } } , \quad x > 0$$
The shaded region is bounded by \(C\), the \(x\)-axis and the lines with equations \(x = 1\) and \(x = 2\). The shaded region is rotated through \(2 \pi\) radians about the \(x\)-axis.
Using calculus, calculate the volume of the solid generated. Give your answer in the form \(\pi ( a + \ln b )\), where \(a\) and \(b\) are constants.
(8)