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Calculate the line integral of the vector field F = (9xy, x, y + z) 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 given by z = 1 - x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. dr curl(F) = = curl curl(F). dS =

Calculate the line integral of the vector field F = (9xy, x, y + z) 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 given by z = 1 - x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. dr curl(F) = = curl curl(F). dS =

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 = (9xy, x, y + z) 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 given by z = 1- x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. F. dr = curl(F) = S cur curl(F). dS = NA NG TO THAT 3-64-200 2004 One Aut
Transcribed Image Text:Calculate the line integral of the vector field F = (9xy, x, y + z) 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 given by z = 1- x² - y² for x² + y² ≤ 1 oriented with an upward-pointing normal. (Use symbolic notation and fractions where needed.) [F. F. dr = curl(F) = S cur curl(F). dS = NA NG TO THAT 3-64-200 2004 One Aut
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