Volume integrals
Multivariable and vector calculus · Mathematics
Study notes
Q: Find the mass of the unit cube [0,1]^3 with density rho = x + y + z. Mass = integral 0 to 1 integral 0 to 1 integral 0 to 1 of (x+y+z) dz dy dx. We computed this before: innermost gives x + y + 1/2, middle gives x + 1, outer gives 3/2. Mass = 3/2 units.