The region \(A\) is bounded by the \(x\)-axis, the curve \(y = x + \sqrt { x }\) for \(0 \leqslant x \leqslant 4\), and the line \(x = 4\). The region \(B\) is bounded by the \(y\)-axis, the curve \(y = x + \sqrt { x }\) for \(0 \leqslant x \leqslant 4\), and the line \(y = 6\). These regions are shown in Fig. 4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3f674569-7e99-4ba8-84f1-a1eb438e30ed-3_572_513_1779_778}
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\caption{Fig. 4}
\end{figure}
- A uniform lamina occupies the region \(A\). Show that the \(x\)-coordinate of the centre of mass of this lamina is 2.56 , and find the \(y\)-coordinate.
- Using your answer to part (i), or otherwise, find the coordinates of the centre of mass of a uniform lamina occupying the region \(B\).