4 In this question you must show detailed reasoning.
\includegraphics[max width=\textwidth, alt={}, center]{17e92314-d7df-49b8-a441-8d18c91dbbb0-03_646_812_312_242} The diagram shows parts of the curves \(y = 3 \sqrt { x }\) and \(y = 4 - x ^ { 2 }\), which intersect at the point ( 1,3 ). The shaded region, bounded by the two curves and the \(y\)-axis, is occupied by a uniform lamina. Determine the exact \(x\)-coordinate of the centre of mass of the lamina.