Application of double integrals: density

[dlevanchuk]

Homework Statement

The boundary of a lamina consists of the semicircles y = sqrt(1-x^2) and y = sqrt(4-x^2) together with the portion of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin

Homework Equations

The Attempt at a Solution

I have a hard time getting y and x boundaries, plus the function that's going to be integraded..
I understand that the function found be the distance from (0,0).. but how can I express that mathematically? I'm thinking that it could be simply sqrt(x^2+y^2), since x and y for a right trinagle, with hypotenuse being the distance to the point..

But with the boundaries - I'm completely lost.. help! :(

 

[dlevanchuk]

Ok, never mind. I got it :) Forgot about the polar coordinates..