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3. Let || P| be the norm of the partition or the length of the longest diagonal of the Dr. A sum of the form Σ-1 F(x, y, z) AV, where (x, y, z) is an arbitrary point within each D and AV denotes the volume of each D, is called a Riemann sum. The type of partition used in step 2, where all the D, lie completely within D, is called an inner partition of D.

3. Let || P| be the norm of the partition or the length of the longest diagonal of the Dr. A sum of the form Σ-1 F(x, y, z) AV, where (x, y, z) is an arbitrary point within each D and AV denotes the volume of each D, is called a Riemann sum. The type of partition used in step 2, where all the D, lie completely within D, is called an inner partition of D.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(x, y, z) FIGURE 9.15.1 Sample point in kth subregion 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. 3. Let || P|| be the norm of the partition or the length of the longest diagonal of the Dr. K-1 A sum of the form Σk=1 F(x, y, z) AV, where (x, yk, zi) is an arbitrary point within each D and AV denotes the volume of each D, is called a Riemann sum. The type of partition used in step 2, where all the D lie completely within D, is called an inner partition of D.
Transcribed Image Text:(x, y, z) FIGURE 9.15.1 Sample point in kth subregion 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. 3. Let || P|| be the norm of the partition or the length of the longest diagonal of the Dr. K-1 A sum of the form Σk=1 F(x, y, z) AV, where (x, yk, zi) is an arbitrary point within each D and AV denotes the volume of each D, is called a Riemann sum. The type of partition used in step 2, where all the D lie completely within D, is called an inner partition of D.
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