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Curve parametrization and triple integration

In the multivariable calculus course, a standard application of triple integration is to find volumes of bounded regions in . 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.