Use the divergence theorem to evaluate the surface integral normal for S. ₂² F. Nd.S where F = xyzi+xyzj+ xyzk, S is the surface of the box 0 ≤x≤1,0 ≤ y ≤ 2,0 ≤ z≤ 3, and N is the outward unit
Use the divergence theorem to evaluate the surface integral normal for S. ₂² F. Nd.S where F = xyzi+xyzj+ xyzk, S is the surface of the box 0 ≤x≤1,0 ≤ y ≤ 2,0 ≤ z≤ 3, and N is the outward unit
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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![Use the divergence theorem to evaluate the surface integral
\[
\iint_S \mathbf{F} \cdot \mathbf{N} \, dS
\]
where \(\mathbf{F} = xyz \mathbf{i} + xyz \mathbf{j} + xyz \mathbf{k}\), \(S\) is the surface of the box \(0 \leq x \leq 1\), \(0 \leq y \leq 2\), \(0 \leq z \leq 3\), and \(\mathbf{N}\) is the outward unit normal for \(S\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F140bd83b-645e-45c3-8644-e53276eab044%2F3fe99c0d-e875-407c-aa6b-29e275c0382e%2F6cgqtlb_processed.png&w=3840&q=75)
Transcribed Image Text:Use the divergence theorem to evaluate the surface integral
\[
\iint_S \mathbf{F} \cdot \mathbf{N} \, dS
\]
where \(\mathbf{F} = xyz \mathbf{i} + xyz \mathbf{j} + xyz \mathbf{k}\), \(S\) is the surface of the box \(0 \leq x \leq 1\), \(0 \leq y \leq 2\), \(0 \leq z \leq 3\), and \(\mathbf{N}\) is the outward unit normal for \(S\).
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