Changing the Order of Integration in Triple Integrals

Changing the order of integration can make a triple integral easier to evaluate without changing the solid region being measured. In this example, the solid is enclosed by a flat base, a slanted plane, two vertical planes, and a parabolic cylinder. The goal is to integrate e^x over this three-dimensional region, so the main task...

Consider a three-dimensional region bounded by a flat base, a slanted plane, two vertical planes, and a parabolic cylinder. The goal is to evaluate the triple integral of e to the power of x over this region.

First, the integral is set up with x as the innermost variable. Here, x varies from the vertical plane t...