Original Articles

Cavalieri integration

Published in: Quaestiones Mathematicae
Volume 35, issue 3, 2012 , pages: 265–296
DOI: 10.2989/16073606.2012.724937
Author(s): E.R. AckermannComputational and Applied Mathematics Department, USA, T.L. GroblerDepartment of Electrical, Electronic and Computer Engineering, South Africa, W. KleynhansDepartment of Electrical, Electronic and Computer Engineering, South Africa, J.C. OlivierSchool of Engineering, Australia, B.P. SalmonDepartment of Electrical, Electronic and Computer Engineering, South Africa, A.J. van ZylDepartment of Mathematics and Applied Mathematics, South Africa

Abstract

We use Cavalieri's principle to develop a novel integration technique which we call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way we can use single Cavalieri integrals to find the areas of some interesting regions for which it is difficult to construct single Riemann integrals.

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