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Volume integral of a function over tetrahedron
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[QUOTE="physkim, post: 5349127, member: 574268"] [h2]Homework Statement [/h2] Calculate the volume integral of the function $$f(x,y,z)=xyz^2$$ over the tetrahedron with corners at $$(0,0,1) (1,0,0) (0,1,0) (0,0,1)$$ [h2]Homework Equations[/h2] 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? [h2]The Attempt at a Solution[/h2] $$\int_{0}^{1} \int_{0}^{1-y} \int_{0}^{1-x-y} xyz^2 dz dx dy =\frac{1}{2520}$$ Big thanks in advance ! [/QUOTE]
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Volume integral of a function over tetrahedron
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