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Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y? with x2 + y2s9 and n is upward.

Evaluate J CurIF. [cariF- nas F(x,v,z) = - yi + xj + zk, and S is part of the sphere z =9-x2 - y? with x2 + y2s9 and n is upward.

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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### Evaluate \( \iint_S \text{Curl} \, \mathbf{F} \cdot \mathbf{n} \, dS \) Given: \[ \mathbf{F}(x,y,z) = -y\mathbf{i} + x\mathbf{j} + z\mathbf{k}, \] and \[ S \text{ is part of the sphere } z = 9 - x^2 - y^2 \text{ with } x^2 + y^2 \leq 9 \text{ and } \mathbf{n} \text{ is upward.} \]
Transcribed Image Text:### Evaluate \( \iint_S \text{Curl} \, \mathbf{F} \cdot \mathbf{n} \, dS \) Given: \[ \mathbf{F}(x,y,z) = -y\mathbf{i} + x\mathbf{j} + z\mathbf{k}, \] and \[ S \text{ is part of the sphere } z = 9 - x^2 - y^2 \text{ with } x^2 + y^2 \leq 9 \text{ and } \mathbf{n} \text{ is upward.} \]
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