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Calculate the line integral of the vector field F= surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y² + z² = 4, z ≥ 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F.dr curl(F) = = curl curl(F). dS = = (y, x, x² + y²) around the boundary curve, the curl of the vector field, and the

Calculate the line integral of the vector field F= surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y² + z² = 4, z ≥ 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F.dr curl(F) = = curl curl(F). dS = = (y, x, x² + y²) around the boundary curve, the curl of the vector field, and the

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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Calculate the line integral of the vector field F = (y, x, x² + y²) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y² + z² = 4, z ≥ 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. F. dr = curl(F) = s curl curl(F). dS =
Transcribed Image Text:Calculate the line integral of the vector field F = (y, x, x² + y²) around the boundary curve, the curl of the vector field, and the surface integral of the curl of the vector field. The surface S is the upper hemisphere x² + y² + z² = 4, z ≥ 0 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. F. dr = curl(F) = s curl curl(F). dS =
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