B D cF I| f(x, y, z) dV = dz d
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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![The image shows the mathematical expression for a triple integral over a region \( R \), written as:
\[
\iiint_R f(x, y, z) \, dV = \int_A^B \int_C^D \int_E^F \, [ \; ] \, dz \, dy \, dx
\]
This equation represents the process of integrating a function \( f(x, y, z) \) over a three-dimensional region \( R \). The limits of integration \( A \) to \( B \), \( C \) to \( D \), and \( E \) to \( F \) indicate the bounds of the region along the \( x \)-, \( y \)-, and \( z \)-axes, respectively. The notation \( dz \, dy \, dx \) specifies the order of integration for the variables. The empty bracket in the inner integral placeholder implies the function to be integrated is not specified, which is typically replaced by the particular function \( f(x, y, z) \) relevant to the context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F32c0095a-f2a0-4d89-b4f6-9114ab30fa27%2Fadf4f3a1-3ac3-4e01-9054-5a3eee9ccaa8%2Flrr0l9b_processed.png&w=3840&q=75)
Transcribed Image Text:The image shows the mathematical expression for a triple integral over a region \( R \), written as:
\[
\iiint_R f(x, y, z) \, dV = \int_A^B \int_C^D \int_E^F \, [ \; ] \, dz \, dy \, dx
\]
This equation represents the process of integrating a function \( f(x, y, z) \) over a three-dimensional region \( R \). The limits of integration \( A \) to \( B \), \( C \) to \( D \), and \( E \) to \( F \) indicate the bounds of the region along the \( x \)-, \( y \)-, and \( z \)-axes, respectively. The notation \( dz \, dy \, dx \) specifies the order of integration for the variables. The empty bracket in the inner integral placeholder implies the function to be integrated is not specified, which is typically replaced by the particular function \( f(x, y, z) \) relevant to the context.
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