We use integrals to model mass.


We learned some time ago that if the density of an object is uniform, When the density of an object is not uniform, we define a density function and mass , to write: Summing these together with an integral, we find the mass is equal to

Moments and center of mass

A moment is a scalar quantity describing how mass is distributed in relation to a point, line, or plane.

The moments are directly related to the center of mass of an object.

As stated before, there are many uses for triple integration beyond finding volume. When describes a rate of change function over some space region , then gives the total change over . Our example of this was computing mass via a density function. Here a density function is simply a “rate of mass change per volume” function. Thus, integrating density gives total mass.

While knowing how to integrate is important, it is arguably much more important to know how to set up integrals. It takes skill to create a formula that describes a desired quantity; modern technology is very useful in evaluating these formulas quickly and accurately.