Bridging Disks and Shells Methods: A Probabilistic Approach

Alexander Vaninsky

Abstract


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

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DOI: http://dx.doi.org/10.26713%2Fjims.v2i1.22

eISSN 0975-5748; pISSN 0974-875X