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Cavalieri integration

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dc.contributor.author Ackermann, ER
dc.contributor.author Grobler, TL
dc.contributor.author Kleynhans, W
dc.contributor.author Olivier, JC
dc.contributor.author Salmon, BP
dc.contributor.author Van Zyl, AJ
dc.date.accessioned 2013-03-25T06:17:34Z
dc.date.available 2013-03-25T06:17:34Z
dc.date.issued 2012-09
dc.identifier.citation Ackermann, ER, Grobler, TL, Kleynhans, W, Olivier, JC, Salmon, BP and Van Zyl, AJ. 2012. Cavalieri integration. Quaestiones Mathematicae, vol. 35(3), pp. 265-296 en_US
dc.identifier.issn 1607-3606
dc.identifier.uri http://www.tandfonline.com/doi/pdf/10.2989/16073606.2012.724937
dc.identifier.uri http://www.tandfonline.com/doi/abs/10.2989/16073606.2012.724937
dc.identifier.uri http://hdl.handle.net/10204/6582
dc.description Copyright: 2012 Taylor & Francis. This is the postprint version of the work. The definitive version is published in Quaestiones Mathematicae, vol. 35(3), pp. 265-296 en_US
dc.description.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). en_US
dc.language.iso en en_US
dc.publisher Taylor & Francis en_US
dc.relation.ispartofseries Workflow;9581
dc.relation.ispartofseries Workflow;9591
dc.subject Cavalieri en_US
dc.subject Method of indivisibles en_US
dc.subject Riemann en_US
dc.subject Riemann-Stieltjes en_US
dc.title Cavalieri integration en_US
dc.type Article en_US
dc.identifier.apacitation Ackermann, E., Grobler, T., Kleynhans, W., Olivier, J., Salmon, B., & Van Zyl, A. (2012). Cavalieri integration. http://hdl.handle.net/10204/6582 en_ZA
dc.identifier.chicagocitation Ackermann, ER, TL Grobler, W Kleynhans, JC Olivier, BP Salmon, and AJ Van Zyl "Cavalieri integration." (2012) http://hdl.handle.net/10204/6582 en_ZA
dc.identifier.vancouvercitation Ackermann E, Grobler T, Kleynhans W, Olivier J, Salmon B, Van Zyl A. Cavalieri integration. 2012; http://hdl.handle.net/10204/6582. en_ZA
dc.identifier.ris TY - Article AU - Ackermann, ER AU - Grobler, TL AU - Kleynhans, W AU - Olivier, JC AU - Salmon, BP AU - Van Zyl, AJ AB - 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). DA - 2012-09 DB - ResearchSpace DP - CSIR KW - Cavalieri KW - Method of indivisibles KW - Riemann KW - Riemann-Stieltjes LK - https://researchspace.csir.co.za PY - 2012 SM - 1607-3606 T1 - Cavalieri integration TI - Cavalieri integration UR - http://hdl.handle.net/10204/6582 ER - en_ZA


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