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. Ackermann Computational and Applied Mathematics Department, USA , T.L. Grobler Department of Electrical, Electronic and Computer Engineering, South Africa , W. Kleynhans Department of Electrical, Electronic and Computer Engineering, South Africa , J.C. Olivier School of Engineering, Australia , B.P. Salmon Department of Electrical, Electronic and Computer Engineering, South Africa , A.J. van Zyl Department of Mathematics and Applied Mathematics, South Africa

Keywords: Cavalieri , method of indivisibles , integration , Riemann , Riemann-Stieltjes , Cavalieri , method of indivisibles , integration , Riemann , Riemann-Stieltjes

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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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