December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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9.15 Triple Integrals
INTRODUCTION
The steps leading to the definition of the three-dimensional definite integral or triple integral are quite similar to the steps leading to the definition of the double integral. Obvious differences: Instead of a function of two variables we are integrating a function f of three variables, not over a region R in a coordinate plane, but over a region D of 3-space.
- Let w = F(x, y, z) be defined over a closed and bounded region D of space.
- By means of a three-dimensional grid of vertical and horizontal planes parallel to the coordinate planes, form a partition P of D into n subregions (boxes) Dk of volumes ΔVk that lie entirely in D.
- Let be the norm of the partition or the length of the longest diagonal of the ...
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