| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2012 |
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| Session | June |
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| Topic | Centre of Mass 2 |
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10 The curve \(C\) has equation
$$y = 2 \left( \frac { x } { 3 } \right) ^ { \frac { 3 } { 2 } }$$
where \(0 \leqslant x \leqslant 3\). Show that the arc length of \(C\) is \(2 ( 2 \sqrt { 2 } - 1 )\).
Find the coordinates of the centroid of the region enclosed by \(C\), the \(x\)-axis and the line \(x = 3\).