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4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = r² + y². (Assume positive or outward orientation for the surface.)

4. (Section 17.8) Use the Divergence Theorem to calculate [[F F-dS, where F = y + ryj – zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = r² + y². (Assume positive or outward orientation for the surface.)

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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I needed help with how to apply divergence theorem for this problem. Setting up the problem and using divergence theorem are things I need a refresher on.

MATH213 - Calculus III Worksheet 14 4. (Section 17.8) Use the Divergence Theorem to calculate •[[F. F-dS, where Fyi+zyj - zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = z² + y². (Assume positive or outward orientation for the surface.)
Transcribed Image Text:MATH213 - Calculus III Worksheet 14 4. (Section 17.8) Use the Divergence Theorem to calculate •[[F. F-dS, where Fyi+zyj - zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = z² + y². (Assume positive or outward orientation for the surface.)
MATH213 - Calculus III Worksheet 14 4. (Section 17.8) Use the Divergence Theorem to calculate •[[F. F-dS, where Fyi+zyj - zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = z² + y². (Assume positive or outward orientation for the surface.)
Transcribed Image Text:MATH213 - Calculus III Worksheet 14 4. (Section 17.8) Use the Divergence Theorem to calculate •[[F. F-dS, where Fyi+zyj - zk and S is the boundary of the region inside the solid cylinder z² + y² ≤ 4, between the plane z = 0 and the paraboloid z = z² + y². (Assume positive or outward orientation for the surface.)
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