8. In Example 4.2 of the Workbook we were asked to find the mass and centre of mass of the-semicircular lamina \left\{x^{2}+y^{2} \leq 1, y \geq 0\right\} if the density

equals the distance r from the origin. We found in class that the mass is M=\pi / 3 and that the coordinates of the centre of mass are- 1.5 \bar{x}=0 \bar{y}=3 / 2 \pi Take care with what these mean. For example, ỹ is the average value of the y-coordinates of all the points in the lamina, where this is a weighted average, each "point" weighted by its mass. Here's the problem: what is 7, the average value of r, over the same semi-circular lamina, and with the same density (equal to the distance r from the origin)?