Title

An alternative way of defining integration in multivariable calculus

Publication Name

International Journal of Mathematical Education in Science and Technology

Abstract

In undergraduate calculus of several variables, double and triple integrals are usually defined as limits of certain Riemann sums. The existence of the integral, as well as the integration formulas, are stated without proof since they require more advanced mathematics. In this article, an alternative and straightforward way of defining multiple integrals is proposed where the usual integration formulas follow as a direct application of the definition. The underlying idea is to map the arbitrary region of integration to an n-dimensional open interval, and integration over the latter is defined via the usual iterated integral. Moreover, the substitution formula is taken as a definition. Numerous illustrative examples are provided.

Open Access Status

This publication is not available as open access

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Link to publisher version (DOI)

http://dx.doi.org/10.1080/0020739X.2022.2095540