Abstract
Although the definition of the integral reflects its origins in scientific problems, its evaluation relies on a considerable range of mathematical concepts and tools. Most fundamental is the change of variables formula; the single-variable version (“u-substitution”) is perhaps the core technique of integration in the introductory calculus course. By contrast, the method of iterated integrals has no singlevariable analogue; it evaluates a double integral by “partial integration” of one variable at a time. This chapter connects double and iterated integrals, establishes the change of variables formula, and discusses Green’s theorem as a tool for evaluating double integrals and as a reason for orienting them.
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© 2010 Springer New York
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Callahan, J.J. (2010). Evaluating Double Integrals. In: Advanced Calculus. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7332-0_9
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DOI: https://doi.org/10.1007/978-1-4419-7332-0_9
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7331-3
Online ISBN: 978-1-4419-7332-0
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