Please see the attached file for the fully formatted problem.
I = integration(over disk area)[(x+y)dA]
For disk of radius R = 4,
x = r*cos(T)
y = r*sin(T)
where, r is the distance of the point (x,y) from the origin and T is the angle of radial ...
A double integral is found using polar coordinates. The solution is concise.