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Evaluating Double Integrals

  • James J. CallahanEmail author
Chapter
Part of the Undergraduate Texts in Mathematics book series (UTM)

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.

Keywords

Variable Formula Computer Algebra System Double Integral Positive Orientation Inverse Function Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSmith CollegeNorthamptonUSA

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