1. The problem statement, all variables and given/known data Find the centre of mass of the 2-dimensional plate which occupies the region inside the circle x2+y2=2y, but outside x2+y2=1, and for which the density is inversely proportional to its distance from the origin. 2. Relevant equations/workings The first circle can be rearranged to give x2+(y-1)2=1, i.e. a circle of radius 1 with centre at (0,1). The last piece of information translates to p=1/(x2+y2)1/2, where p = density. The formula for mass of this plate will be a double integral of p over the given area. Sketching a diagram, we can see that this area is the upper part of the first circle, (i.e. the area of the first circle minus the intersecting area of two circles). Once we have the mass, centre of mass is discernible via other formulae. I basically need help to know what my upper and lower values should be to integrate over for x and y, and also how to initially integrate p with respect to y... this should yield a trig or log function, right?