id: 06228775
dt: j
an: 2014e.00680
au: Ackermann, E.R.; Grobler, T.L.; Kleynhans, W.; Olivier, J.C.; Salmon, B.P.;
van Zyl, A.J.
ti: Cavalieri integration.
so: Quaest. Math. 35, No. 3, 265-296 (2012).
py: 2012
pu: Taylor \& Francis, Abingdon, Oxfordshire; National Inquiry Services Centre
(NISC), Grahamstown
la: EN
cc: I55
ut: Cavalieri integral; Riemann integral; Riemann-Stieltjes integral;
integration; method of indivisibles
ci:
li: doi:10.2989/16073606.2012.724937
ab: 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 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 $g(x)$.
rv: