In Double Integrals over Rectangular Regions, we discussed the double integral of a function [latex]f(x,y)[/latex] of two variables over a rectangular region in the plane. In this section we define the triple integral of a function [latex]f(x,y,z)[/latex] of three variables over a rectangular solid box in space, [latex]\mathbb{R}^{3}[/latex]. Later in this section we extend the definition to more general regions in [latex]\mathbb{R}^{3}[/latex].