A uniform lamina is in the shape of the region $$\(R\)$$. Region $$\(R\)$$ is bounded by the curve with equation $$\(y=x(x+a)\)$$ where $$\(a\)$$ is a positive constant, the positive $$\(x\)$$-axis and the line with equation $$\(x=a\)$$, as shown shaded in Figure 1. Find the $$\(y\)$$ coordinate of the centre of mass of the lamina. (7)

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