Some Triple Integrals for Mass
Some Triple Integrals for Mass
For an object with uniform density, the mass can be calculated as density times volume . For an object with nonuniform density, calculus is necessary. The idea is to partition the object into enough small cubes so that the density of each cube is approximately uniform. Then, the mass of the object, which is the sum of the masses of each of the cubes, can be approximated by the sum of the density times volume for each individual cube (i.e. if the object is partitioned into cubes with density and volume , then the mass of the object is ). The exact mass is the triple integral of the density function.
(m=ρv)
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