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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 + z³k, S is the part of the cone z = √√√x² + y² between the planes z = 1 and z = 4 with downward orientation z= 70√2π × xx 0 z = 4

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 = √√√x² + y² between the planes z = 1 and z = 4 with downward orientation z= 70√2π × xx 0 z = 4

Algebra & Trigonometry with Analytic Geometry
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 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 = √√√x² + y² between the planes z = 1 and z = 4 with downward orientation z= 70√2π × xx 0 z = 4
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 = √√√x² + y² between the planes z = 1 and z = 4 with downward orientation z= 70√2π × xx 0 z = 4
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