Curve parametrization and triple integration

Abstract

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in ${\mathbf{R}}^3$. In this article, we consider the problem of computing volumes, by way of examples, of regions bounded by planes and quadric surfaces. For illustration, we present the solution to two basic but non-standard problems. The analysis employed shows how the parametrization of the intersection curves is obtained and used in setting up the volume integrals.

Keywords:

• Undergraduate calculus education
• triple integrals
• curve parametrization

Acknowledgments

The authors wish to thank the referees for their comments.

Disclosure statement

No potential conflict of interest was reported by the authors.