A lamina occupies the region inside the circle x^2 + y^2 = 2y but outside the circle x^2 + y^2 = 1. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.
Xcm = double integral of y*f(x,y)
Ycm = double integral of x*f(x,y)
The Attempt at a Solution
I know my integrand will be k(constant)/r
and I know how to solve for centre of mass, my only trouble is setting up the double integral. I think these are circles centred at 2 and 0, and when I draw them in cartesian coords, my region R is the space in between them that looks like a crescent moon. I don't know how to set up my double integral, because I can't express the first circle in terms of y, since there are two terms of them. Please help?