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Answers for “在这个三重积分课程中,$\rho(x,y,z)=xyz$ 意味着什么?”

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The differential mass element dmassdmass is derived by multiplying the local density ρ(x,y,z)\rho(x,y,z) by the infinitesimal volume element dVdV. For the example density ρ(x,y,z)=xyz\rho(x,y,z)=xyz, this gives dmass=xyz dVdmass = xyz \, dV.

Conditions: The object has non-uniform density.; The density is modeled as a function of position (x,y,z)(x,y,z).; dVdV denotes an infinitesimal volume element.