I am suppose to determine the center of mass for a metal plate that is bound by the curve y = x^2 and the x axis. with x equal or greater than 0 and equal or less than 1. There is a constant density of 2 gm/cm^2.

I got the total mass was equal to the integral from 0 to 1 of 2dx therefore it is 2 gm.

For center of mass I think I would take the integral between 0 and 1 of the density times the area times x dx. Would my area be the integral of x^2 from 0 to 1? I get a center of mass of 2/15 and the answer should be 2/3 gm. Any help would be greatly appreciated. Thanks, Frostking