Evaluate the surface integral JSF 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 = 6

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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Evaluate the surface integral
JSF
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 = 6
Transcribed Image Text:Evaluate the surface integral JSF 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 = 6
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