The region enclosed by the curve with equation \(y = \frac { 1 } { 2 } \sqrt { x }\), the \(x\)-axis and the lines \(x = 2\) and \(x = 4\), is rotated through \(2 \pi\) radians about the \(x\)-axis to form a uniform solid \(S\). Use algebraic integration to find the exact value of the \(x\) coordinate of the centre of mass of \(S\).
(6)