For the vector field F(x, y, z) = (2y — 1) 7+ (z² + 2xz)J+2xyk - the line integral over the curve C: x² + y² = 9 at z = 0 yields f F · dr = −18π. $ State Stokes' theorem and then verify Stokes' theorem in this case by calcu- lating the surface integral over the paraboloid z = 9 - (x² + y²) above the xy-plane.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
Question
For the vector field
F(x, y, z) = (2y — 1) 7+ (z² + 2xz)J+2xyk
-
the line integral over the curve C: x² + y² = 9 at z = 0 yields
f F · dr = −18π.
$
State Stokes' theorem and then verify Stokes' theorem in this case by calcu-
lating 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) 7+ (z² + 2xz)J+2xyk - the line integral over the curve C: x² + y² = 9 at z = 0 yields f F · dr = −18π. $ State Stokes' theorem and then verify Stokes' theorem in this case by calcu- lating the surface integral over the paraboloid z = 9 - (x² + y²) above the xy-plane.
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