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For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.

For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.

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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For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.
Transcribed Image Text:For the vector field F(x, y, z) = (2y-1) + (2² + 2x2)J+2xyk the line integral over the curve C: x²+ y² = 9 at 2 = 0 yields == f F³ · dr = − 18πT. State Stokes' theorem and then verify Stokes' theorem in this case by calculating the surface integral over the paraboloid z = 9 (x² + y²) above the xy-plane.
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