Grobler, TLAckermann, ERVan Zyl, AJOlivier, JC2011-11-082011-11-082011-10Grobler, TM, Ackermann, ER, Van Zyl, AJ et.al. 2011. Cavalieri Integration. CSIR Technical reporthttp://hdl.handle.net/10204/5267This is a CSIR Technical report. Permission to self archive has been granted by the CSIR researchersThe authors use Cavalieri's principle to develop a novel integration technique which they call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way they can use single Cavalieri integrals to find the areas of some interesting regions for which it is difficult to construct single Riemann integrals. They 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).enCavalieri integrationIrregular integration shapesRiemann integralsReportGrobler, T., Ackermann, E., Van Zyl, A., & Olivier, J. (2011). <i>Cavalieri Integration - CSIR Technical report</i> (Workflow request;7518). CSIR. Retrieved from http://hdl.handle.net/10204/5267Grobler, TL, ER Ackermann, AJ Van Zyl, and JC Olivier <i>Cavalieri Integration - CSIR Technical report.</i> Workflow request;7518. CSIR, 2011. http://hdl.handle.net/10204/5267Grobler T, Ackermann E, Van Zyl A, Olivier J. Cavalieri Integration - CSIR Technical report. 2011 [cited yyyy month dd]. Available from: http://hdl.handle.net/10204/5267TY - Report AU - Grobler, TL AU - Ackermann, ER AU - Van Zyl, AJ AU - Olivier, JC AB - The authors use Cavalieri's principle to develop a novel integration technique which they call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that non-rectangular integration strips are used. In this way they can use single Cavalieri integrals to find the areas of some interesting regions for which it is difficult to construct single Riemann integrals. They 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 - 2011-10 DB - ResearchSpace DP - CSIR KW - Cavalieri integration KW - Irregular integration shapes KW - Riemann integrals LK - https://researchspace.csir.co.za PY - 2011 T1 - Cavalieri Integration - CSIR Technical report TI - Cavalieri Integration - CSIR Technical report UR - http://hdl.handle.net/10204/5267 ER -