Standard +0.3 This is a straightforward application of standard centre of mass formulas for a lamina bounded by a curve. The function y = √x is simple to integrate (giving x^(3/2) and x^(5/2) terms), the limits are clean constants, and the method is a direct textbook procedure requiring no problem-solving insight. Slightly easier than average due to the routine nature and simple integrand.
2 The region enclosed by the curve \(y = \sqrt { } x\) for \(0 \leqslant x \leqslant 9\), the \(x\)-axis and the line \(x = 9\) is occupied by a uniform lamina. Find the coordinates of the centre of mass of this lamina.
2 The region enclosed by the curve $y = \sqrt { } x$ for $0 \leqslant x \leqslant 9$, the $x$-axis and the line $x = 9$ is occupied by a uniform lamina. Find the coordinates of the centre of mass of this lamina.
\hfill \mbox{\textit{OCR M4 2005 Q2 [7]}}