Explain how to find the center of mass of a

Solution 5E

To find the center of mass of a three-dimensional object with a variable density, we use triple integral.

First we need to find the three moments, then we divide each moment by the mass. And, to find the mass we integrate the density function over the volume occupied by the object, using triple integral.

“If is a density function on a closed bounded region in , then the center of mass of the region is given by