TEX document #3

M = ∫_{E} ρ dV.

We can do the integrations over the three coordinates in any order we choose. Here we have chosen to do the the z integral first (that is, put it on the inside), then y, then x.

M = ∫_{0}^{1} [∫_{0}^{1} [∫_{0}^{2}(1 + 2y) dz] dy] dx

= ∫_{0}^{1} ∫_{0}^{1}[(1 + 2y)z]_{z=0}^{2} dy dx

= ∫_{0}^{1} ∫_{0}^{1} 2(1 + 2y) dy dx

= 2 ∫_{0}^{1}[y + y^{2}]_{0}^{1} dx

= 2 ∫_{0}^{1}(1 + 1) dx

= 4 ∫_{0}^{1} dx

= 4 kg.