]] F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across Evaluate the surface integral 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+ u sin vj+vk, 0≤u≤ 3,0 ≤ v≤ 2π

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

16.7 #10

Evaluate the surface integral
J
F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across
S
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+ u sin vj + v k, 0 ≤ u ≤ 3,0 ≤ v ≤ 2π
Transcribed Image Text:Evaluate the surface integral J F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S 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+ u sin vj + v k, 0 ≤ u ≤ 3,0 ≤ v ≤ 2π
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