| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2009 |
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| Session | June |
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| Topic | Centre of Mass 2 |
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3 The equation of a curve is \(y = \lambda x ^ { 2 }\), where \(\lambda > 0\). The region bounded by the curve, the \(x\)-axis and the line \(x = a\), where \(a > 0\), is denoted by \(R\). The \(y\)-coordinate of the centroid of \(R\) is \(a\). Show that \(\lambda = \frac { 10 } { 3 a }\).