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 x^2+y^2=2x, but outside x^2+y^2=1, and for which the density is proportional to its distance from the origin. 2. Relevant equations Centre of mass for x coordinate: 1/m ∫∫ x ρ(x,y) DA 3. The attempt at a solution I have already calculated the mass which turned out to be 8/3 by integrating and subtracting the two circle to obtain the area where they intersects. I am now trying to find the centre of mass, the y-coord is 0 as it is symmetrical about the x-axis. To calculate the centre of mass i am using this domain in polar coord: 1 ≤ r ≤ 2 cos θ and π/6 ≤ θ ≤ 5π/6 With the domain above my equation is: 3/8 ∫∫ x(Kr) r dr dθ = 3/8 ∫∫ (r cos θ)(Kr) r dr dθ Is this correct? I was doing the working, i couldn't get any answer because it didn't make much sense to me, and i was sure i am doing something wrong somewhere. Do you guys mind advising me on where i have gone wrong? Thank you very much!