Bridging Disks and Shells Methods: A Probabilistic Approach (Journal of Informatics and Mathematical Sciences, 2010)
Consideration of a function shaping the surface of a solid of revolution as a random variable allows for extension of the proof that the disks and the shells methods give the same result from monotonic continuous functions to a subclass of Riemann-integrable functions.
Keywords: Probabilistic approach in calculus; Elementary and piecewise elementary functions as random variables; Integration by parts for Riemann and Lebesgue-Stieltjes integrals; Volumes of solids of revolution; Disks and shells methods equivalence