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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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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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