1.
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\includegraphics[alt={},max width=\textwidth]{bd1e2b07-4a87-49d6-addd-c9f67467ef2f-02_472_750_255_660}
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\caption{Figure 1}
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A uniform lamina is in the shape of the region \(R\).
Region \(R\) is bounded by the curve with equation \(y = x ( x + a )\) where \(a\) is a positive constant, the positive \(x\)-axis and the line with equation \(x = a\), as shown shaded in Figure 1.
Find the \(\boldsymbol { y }\) coordinate of the centre of mass of the lamina.