1. The problem statement, all variables and given/known data For a particular material the density varies with position as ρ(r)=x2yz Find the total mass of a unit cube with one edge in the origin made by a such a material. 2. Relevant equations We have dm = ρ(r)dV = ρ(r)dxdydz So we want to calculate the volume integral (all from 0 to 1): ∫∫∫x2yz dxdydz = 1/12 First of all: Is this correct? Now if so, my problem is just that I don't find the approach quite intuitive. You want to sum up all small volume contributions. What is that then makes you able to split the integral into integration over 3 directions? Can you explain to me what happens intuitively?