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Use Stokes Theorem to evaluate where F(z, y, z) = (y cos(2), -e* sin(2), 2ze) and S is the hemisphere z² + y² +2²=9, 220, oriented upwards. Since the hemisphere is oriented upwards the boundary curve must be transversed ? when viewed from above. A parametrization for the boundary curve C can be given by: r(t) = 3 cos(t)i+ Σ j+ curl curl F.dS= das = fr If curl •ff₁² curl F.dS= curl F. dS M dt Σ K, 0 << Σ (use the most natural parametrization)

Use Stokes Theorem to evaluate where F(z, y, z) = (y cos(2), -e* sin(2), 2ze) and S is the hemisphere z² + y² +2²=9, 220, oriented upwards. Since the hemisphere is oriented upwards the boundary curve must be transversed ? when viewed from above. A parametrization for the boundary curve C can be given by: r(t) = 3 cos(t)i+ Σ j+ curl curl F.dS= das = fr If curl •ff₁² curl F.dS= curl F. dS M dt Σ K, 0 << Σ (use the most natural parametrization)

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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Use Stokes Theorem to evaluate / curl where F(z, y, z) = (y cos(2), -e* sin(2), 2ze) and S is the hemisphere z² + y² +2²=9, z20, oriented upwards. when viewed from above. Since the hemisphere is oriented upwards the boundary curve must be transversed ? A parametrization for the boundary curve C can be given by: r(t) = 3 cos(t) i+ Σ j+ - ds = f •ffs curl F.dS== curl F.dS= curl F. dS Edt M Ek, Osts M (use the most natural parametrization)
Transcribed Image Text:Use Stokes Theorem to evaluate / curl where F(z, y, z) = (y cos(2), -e* sin(2), 2ze) and S is the hemisphere z² + y² +2²=9, z20, oriented upwards. when viewed from above. Since the hemisphere is oriented upwards the boundary curve must be transversed ? A parametrization for the boundary curve C can be given by: r(t) = 3 cos(t) i+ Σ j+ - ds = f •ffs curl F.dS== curl F.dS= curl F. dS Edt M Ek, Osts M (use the most natural parametrization)
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