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Use Stokes' Theorem to evaluate Scurl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 1 − x2 − y2 that lies above the xy-plane, oriented upward

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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Question

Use Stokes' Theorem to evaluate

curl F · dS.

F(x, y, z) = x² sin(z)i + y²j + xyk,

S is the part of the paraboloid

z = 1 − x² − y²

that lies above the xy-plane, oriented upward.

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