Ackermann, ERGrobler, TLKleynhans, WOlivier, JCSalmon, BPVan Zyl, AJ2013-03-252013-03-252012-09Ackermann, ER, Grobler, TL, Kleynhans, W, Olivier, JC, Salmon, BP and Van Zyl, AJ. 2012. Cavalieri integration. Quaestiones Mathematicae, vol. 35(3), pp. 265-2961607-3606http://www.tandfonline.com/doi/pdf/10.2989/16073606.2012.724937http://www.tandfonline.com/doi/abs/10.2989/16073606.2012.724937http://hdl.handle.net/10204/6582Copyright: 2012 Taylor & Francis. This is the postprint version of the work. The definitive version is published in Quaestiones Mathematicae, vol. 35(3), pp. 265-296We 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).enCavalieriMethod of indivisiblesRiemannRiemann-StieltjesArticleAckermann, E., Grobler, T., Kleynhans, W., Olivier, J., Salmon, B., & Van Zyl, A. (2012). Cavalieri integration. http://hdl.handle.net/10204/6582Ackermann, ER, TL Grobler, W Kleynhans, JC Olivier, BP Salmon, and AJ Van Zyl "Cavalieri integration." (2012) http://hdl.handle.net/10204/6582Ackermann E, Grobler T, Kleynhans W, Olivier J, Salmon B, Van Zyl A. Cavalieri integration. 2012; http://hdl.handle.net/10204/6582.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 -