F(x, y, z) = zexyi - 3zej + xyk, s

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
1/²
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) = zexyi - 3zej + xyk, S is the parallelogram with parametric equations x = u + v₁y = u - v, z = 1+ 2u + v, 0 ≤us 2,0 ≤ vs 1 with upward orientation
F. ds =
Transcribed Image Text:Evaluate the surface integral 1/² 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) = zexyi - 3zej + xyk, S is the parallelogram with parametric equations x = u + v₁y = u - v, z = 1+ 2u + v, 0 ≤us 2,0 ≤ vs 1 with upward orientation F. ds =
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