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Use Stokes' theorem to evaluate // (V × F) · dS where F(x, y, z) = −12yzi + 12xzj + 19(x² + y²)zk and S is the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 1, oriented upward.

Use Stokes' theorem to evaluate // (V × F) · dS where F(x, y, z) = −12yzi + 12xzj + 19(x² + y²)zk and S is the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 1, oriented 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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e ſſ (V × F) · dS where F(x, y, z) = −12yzi + 12xzj + 19(x² + y²)zk and S is the part of the paraboloid z = x² + y² that Use Stokes' theorem to evaluate lies inside the cylinder x² + y² = 1, oriented upward.
Transcribed Image Text:e ſſ (V × F) · dS where F(x, y, z) = −12yzi + 12xzj + 19(x² + y²)zk and S is the part of the paraboloid z = x² + y² that Use Stokes' theorem to evaluate lies inside the cylinder x² + y² = 1, oriented upward.
Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z = 25 - x² for 0 ≤ x ≤ 5 and −5 ≤ y ≤ 5, oriented upward. Sketch both S and its boundary C. Circulation F.dr=
Transcribed Image Text:Use Stokes' Theorem to find the circulation of F = (xy, yz, xz) around the boundary of the surface S given by z = 25 - x² for 0 ≤ x ≤ 5 and −5 ≤ y ≤ 5, oriented upward. Sketch both S and its boundary C. Circulation F.dr=
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