Explain how to find the center of mass of a thin plate

Solution 3E

To find the center of mass of a thin plate with a variable density, we use double integral.
First we need to find the moments about both the - and - axes along with the masses, then we divide each moment by the mass to find the center of mass of a thin plate.
And, to find mass we integrate the density function over the region occupied by the plate, using double integral.

        If  is a density function