How do I find the center of mass using polar coordinates?

[vadar]

Help! I've been trying to do this for ages, but i know there's some silly little thing I am 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.