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Heterogeneous materials

If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: ρ (r →) = d m / d V {\displaystyle \rho ({\vec {r}})=dm/dV}, where d V {\displaystyle dV} is an elementary volume at position r → {\displaystyle {\vec {r}}}. The mass of the body then can be expressed as m = ∫ V ρ (r →) d V. {\displaystyle m=\int _{V}\rho ({\vec {r}})\,dV.}