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Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of the surface z = 9 - x² - y² with > 0 oriented so that n(0,0,9) = (0,0,1). (b) F(x, y, z) = (x, y, 2) and S is the part of the ellipsoid ² + y² + z² = 1 with x, y, z ≥ 0 oriented so that n(0, 0, 1) = (0, 0, 1).

Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of the surface z = 9 - x² - y² with > 0 oriented so that n(0,0,9) = (0,0,1). (b) F(x, y, z) = (x, y, 2) and S is the part of the ellipsoid ² + y² + z² = 1 with x, y, z ≥ 0 oriented so that n(0, 0, 1) = (0, 0, 1).

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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Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of the surface z = 9 - x² - y² with > 0 oriented so that n(0,0,9) = (0,0,1). (b) F(x, y, z) = (x, y, 2) and S is the part of the ellipsoid ² + y² + z² = 1 with x, y, z ≥ 0 oriented so that n(0, 0, 1) = (0, 0, 1).
Transcribed Image Text:Evaluate the following surface integrals [ F. ds. (a) F(x, y, z) = (x, y, z) and S is the part of the surface z = 9 - x² - y² with > 0 oriented so that n(0,0,9) = (0,0,1). (b) F(x, y, z) = (x, y, 2) and S is the part of the ellipsoid ² + y² + z² = 1 with x, y, z ≥ 0 oriented so that n(0, 0, 1) = (0, 0, 1).
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