The definition of the center of mass is
In your case and
Of course, because of symmetry
The question states . Find the center of mass of the lamina x^2 + y^2 less than equal to 1 if the density at any point is proportional to the square of it's distance from the origin.
My question is, what in the crap is the question stating in layman terms? I'm terrible at word problems and need to have this broken down completely.
is the unit disc (centre at the origin), density proportional to the square of distance from origin, means that the desity is a radial function, and as the origin is the centre of the disk without integration we know that the centre of mass is the origin (by symmetry).