2. The finite region bounded by the \(x\)-axis, the curve with equation \(y = 2 \mathrm { e } ^ { x }\), the \(y\)-axis and the line \(x = 1\) is rotated through one complete revolution about the \(x\)-axis to form a uniform solid. Use algebraic integration to

1. show that the volume of the solid is \(2 \pi \left( \mathrm { e } ^ { 2 } - 1 \right)\),
2. find, in terms of e, the \(x\) coordinate of the centre of mass of the solid.