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Cavalieri integration

Citation

Ackermann, ER and Grobler, TL and Kleynhans, W and Olivier, JC and Salmon, BP and van Zyl, AJ, Cavalieri integration, Quaestiones Mathematicae, 35, (3) pp. 265-296. ISSN 1607-3606 (2012) [Refereed Article]

Copyright Statement

Copyright 2012 NISC Pty Ltd

DOI: doi:10.2989/16073606.2012.724937

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.

We also present two methods of evaluating a Cavalieri integral by first transforming it to either an equivalent Riemann or Riemann-Stieltjes integral by using special transformation functions h(x) and its inverse g(x), respectively. Interestingly enough it is often very difficult to find the transformation function h(x), whereas it is very simple to obtain its inverse g(x).

Item Details

Item Type:Refereed Article
Keywords:Cavalieri integration, method of indivisibles, integration, Riemann, Riemann-Stieltjes
Research Division:Mathematical Sciences
Research Group:Pure Mathematics
Research Field:Pure Mathematics not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Olivier, JC (Professor JC Olivier)
Author:Salmon, BP (Dr Brian Salmon)
ID Code:82331
Year Published:2012
Web of Science® Times Cited:2
Deposited By:Engineering
Deposited On:2013-01-25
Last Modified:2015-07-13
Downloads:0

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