for the given vector field F and the oriented surface S. In other words, find the F(x, y, z) = zexi - 3zej + xyk, S is the parallelogram with parametric equations x=u+v₁y=u - v₁ z = 1+2u+v, 0≤u≤ 2,0 ≤ v≤ 1 with upward orientation F. ds = Evaluate the surface integralFds flux of F across S. For closed surfaces, use the positive (outward) orientation. 1/²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Evaluate the surface integral
¹1/₁²
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 + v, y = u - v,
z = 1+ 2u + v, 0≤u≤ 2,0 ≤ v ≤ 1 with upward orientation
S/S F
F. ds =
Transcribed Image Text:Evaluate the surface integral ¹1/₁² 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 + v, y = u - v, z = 1+ 2u + v, 0≤u≤ 2,0 ≤ v ≤ 1 with upward orientation S/S F F. ds =
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