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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Answered: Use the divergence theorem to evaluate…

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 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