
06228775
j
2014e.00680
Ackermann, E.R.
Grobler, T.L.
Kleynhans, W.
Olivier, J.C.
Salmon, B.P.
van Zyl, A.J.
Cavalieri integration.
Quaest. Math. 35, No. 3, 265296 (2012).
2012
Taylor \& Francis, Abingdon, Oxfordshire; National Inquiry Services Centre (NISC), Grahamstown
EN
I55
Cavalieri integral
Riemann integral
RiemannStieltjes integral
integration
method of indivisibles
doi:10.2989/16073606.2012.724937
Summary: We use Cavalieri's principle to develop a novel integration technique which we call Cavalieri integration. Cavalieri integrals differ from Riemann integrals in that nonrectangular 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 RiemannStieltjes 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 $g(x)$.