Advanced Engineering Mathematics, 7th Edition

9.10 Double Integrals

INTRODUCTION

In Section 9.8 we gave the five steps leading to the definition of the definite integral The analogous steps that lead to the concept of the two-dimensional definite integral, known simply as the double integral of a function f of two variables, will be given next.

1. Let z = f(x, y) be defined in a closed and bounded region R of 2-space.
2. By means of a grid of vertical and horizontal lines parallel to the coordinate axes, form a partition P of R into n rectangular subregions R_k of areas ΔA_k that lie entirely in R.
3. Let P be the norm of the partition or the length of the longest diagonal of the R_k.
4. Choose a sample ...