Polar Co-ordinate intergral

[vadar]

Help! Ive been trying to do this for ages, but i know theres some silly little thing im doing wrong!
Problem, Find the center of mass of a constant density semicircular plate of radius a, using polar co-ordinates, what regions do i use for the double intergral with respect to r and θ??????

[J77]

The angle \theta from 0 to \pi, and the radius from 0 to a.

The dA part of the double integration becomes r dr d \theta

You assume uniform density, so you just intgrating r\cos\theta and r\sin\theta to get the coordinates to the centre of mass.