7. The finite region \(R\) is bounded by the curve with equation \(y = x + \frac { 2 } { x }\), the \(x\)-axis and the lines \(x = 1\) and \(x = 4\).
- Find the exact area of \(R\).
The region \(R\) is rotated completely about the \(x\)-axis.
- Find the volume of the solid formed, giving your answer in terms of \(\pi\).