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## Homework Statement

Calculate the volume integral of the function $$f(x,y,z)=xyz^2$$

over the tetrahedron with corners at $$(0,0,1) (1,0,0) (0,1,0) (0,0,1)$$

## Homework Equations

I was able to solve it mathematically, but still can't figure out why the answer is so small.

I only understand that if f(x,y,z) is the density, then the triple integral is the mass.

What is the physical significance for calculating the volume integral of an arbitrary function over a geometrical shape?

## The Attempt at a Solution

$$\int_{0}^{1} \int_{0}^{1-y} \int_{0}^{1-x-y} xyz^2 dz dx dy =\frac{1}{2520}$$

Big thanks in advance !