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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) = yi-xj+z² k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos vi+usin vj + vk, 0 ≤u≤ 4,0 ≤ v ≤ 4π

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) = yi-xj+z² k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos vi+usin vj + vk, 0 ≤u≤ 4,0 ≤ v ≤ 4π

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate the surface integral JI 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. S F(x, y, z) = yi-xj+z²k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos vi + u sin v j + v k, 0 ≤ u ≤ 4,0 ≤ v ≤ 4TT
Transcribed Image Text:Evaluate the surface integral JI 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. S F(x, y, z) = yi-xj+z²k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos vi + u sin v j + v k, 0 ≤ u ≤ 4,0 ≤ v ≤ 4TT
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