1. Evaluate f.dr for F(x, y, z) = −yî + xĵ - 2k for the boundary of the surface S:z² = x² + y², 0 ≤ Z ≤ 4, oriented downward, using Stokes' Theorem. 2. Evaluate the flux ffs ·ds for F(x, y, z) = (cos z + xy²)î + xe¯²ĵ + (siny + x²z)k, where S is the surface of the solid bounded by the paraboloid z = x² + y² and the plane z = 4.

1. Evaluate f.dr for F(x, y, z) = −yî + xĵ - 2k for the boundary of the surface S:z² = x² + y², 0 ≤ Z ≤ 4, oriented downward, using Stokes' Theorem. 2. Evaluate the flux ffs ·ds for F(x, y, z) = (cos z + xy²)î + xe¯²ĵ + (siny + x²z)k, where S is the surface of the solid bounded by the paraboloid z = x² + y² and the plane z = 4.

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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