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Consider the cylinder x² + y² = 1, and let S₁ be the part of the cylinder that lies between the planes z = 0 and z = 2, and S₂ be the part of the plane z = 0 that lies inside the cylinder. Finally, let S = S₁ U S₂ (so S looks like a can with a bottom but no top). If S is oriented inward, use Stokes' Theorem to compute SVxF.ds where F(x, y, z) = (xyz, xz, xy)

Consider the cylinder x² + y² = 1, and let S₁ be the part of the cylinder that lies between the planes z = 0 and z = 2, and S₂ be the part of the plane z = 0 that lies inside the cylinder. Finally, let S = S₁ U S₂ (so S looks like a can with a bottom but no top). If S is oriented inward, use Stokes' Theorem to compute SVxF.ds where F(x, y, z) = (xyz, xz, xy)

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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Consider the cylinder x² + y² = 1, and let S₁ be the part of the cylinder that lies between the planes z = 0 and z = 2, and S₂ be the part of the plane z = 0 that lies inside the cylinder. Finally, let S = S₁ U S₂ (so S looks like a can with a bottom but no top). If S is oriented inward, use Stokes' Theorem to compute S VxF.ds where F(x, y, z) = (xyz, xz, xy)
Transcribed Image Text:Consider the cylinder x² + y² = 1, and let S₁ be the part of the cylinder that lies between the planes z = 0 and z = 2, and S₂ be the part of the plane z = 0 that lies inside the cylinder. Finally, let S = S₁ U S₂ (so S looks like a can with a bottom but no top). If S is oriented inward, use Stokes' Theorem to compute S VxF.ds where F(x, y, z) = (xyz, xz, xy)
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