Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xi + yj + 7k, S is the boundary of the region enclosed by the cylinder x² + z² = 1 and the planes y = 0 and x + y = 3

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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Evaluate the surface integral
F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = xi + yj + 7k, S is the boundary of the region enclosed by the cylinder x² + z² = 1 and the planes y = 0 and x + y = 3
Transcribed Image Text:Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xi + yj + 7k, S is the boundary of the region enclosed by the cylinder x² + z² = 1 and the planes y = 0 and x + y = 3
Evaluate the surface integral
F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = -xi - yj + z³k, S is the part of the cone z =
z = √√x² + y².
0
z = 2
-z=1
x² + y2 between the planes z = 1 and z = 2 with downward orientation
Transcribed Image Text:Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi - yj + z³k, S is the part of the cone z = z = √√x² + y². 0 z = 2 -z=1 x² + y2 between the planes z = 1 and z = 2 with downward orientation
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