Advanced Calculus pp 317-386 | Cite as

# Evaluating Double Integrals

## 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## Preview

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