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CHAPTER 14 Multiple Integrals 14.1 Double Integrals ...

Contents CHAPTER 14 Multiple Integrals Double Integrals Changing to Better Coordinates Triple Integrals Cylindrical and Spherical Coordinates CHAPTER 15 Vector Calculus Vector Fields Line Integrals Green's Theorem Surface Integrals The Divergence Theorem Stokes' Theorem and the Curl of F. CHAPTER 16 Mathematics after Calculus Linear Algebra Differential Equations Discrete Mathematics Study Guide For CHAPTER 1. Answers to Odd-Numbered Problems Index Table of Integrals C H A P T E R 14. Multiple Integrals Double Integrals 4. This CHAPTER shows how to integrate functions of two or more variables. First, a Double integral is defined as the limit of sums. Second, we find a fast way to compute it. The key idea is to replace a Double integral by two ordinary "single" Integrals . The Double integral f(x, y)dy dx starts with 1f(x, y)dy.

The double integral JSf(x, y)dy dx will now be reduced to single integrals in y and then x. (Or vice versa. Our first integral could equally well be ff(x, y)dx.) Chapter 8 described the same idea for solids of revolution. First came the area of a slice, which is a single integral. Then came a second integral to add up the slices.

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