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Stokes' theorem to write a line integral that is equal to the surface integral curl F. dS, whe

Stokes' theorem to write a line integral that is equal to the surface integral curl F. dS, whe

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Use Stokes' theorem to write a line integral that is equal to the surface integral f S F(x, y, z) = (4y -z,-3z, 3x - 4y), S is the portion of the paraboloid z = 9-x² - y² above the xy-plane, and its boundary C' is directed counterclockwise when viewed from the first octant. (Hint: parameterize C by the angle 0, when 0 ≥ 0.) Provide your answer below: curl F. dS, where de
Transcribed Image Text:Use Stokes' theorem to write a line integral that is equal to the surface integral f S F(x, y, z) = (4y -z,-3z, 3x - 4y), S is the portion of the paraboloid z = 9-x² - y² above the xy-plane, and its boundary C' is directed counterclockwise when viewed from the first octant. (Hint: parameterize C by the angle 0, when 0 ≥ 0.) Provide your answer below: curl F. dS, where de
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