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Cavalieri integration

journal contribution
posted on 2023-05-17, 15:36 authored by Ackermann, ER, Grobler, TL, Kleynhans, W, Jan OlivierJan Olivier, Brian SalmonBrian Salmon, van Zyl, AJ

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).

History

Publication title

Quaestiones Mathematicae

Volume

35

Pagination

265-296

ISSN

1607-3606

Department/School

School of Engineering

Publisher

Taylor & Francis

Place of publication

London, UK

Rights statement

Copyright 2012 NISC Pty Ltd

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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