# Find the center of mass of a lamina

The boundary of a lamina consists of the semicircles $y=\sqrt{1-x^2}\ and\ y=\sqrt{4-x^2}$ together with the portions 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.
$\rho=kr$
the bounds are $0\le \theta\le \pi$ while $1\le r\le 2$