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.3 Evaluate || F · dS, where F = < y, – x, z x, z° > and S is the helicoid with vector equation r(u, v) = < u cos v, u sin v, v > 0

.3 Evaluate || F · dS, where F = < y, – x, z x, z° > and S is the helicoid with vector equation r(u, v) = < u cos v, u sin v, v > 0

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 dS, where < y, – x, z³ > and S'is S the helicoid with vector equation r(и, v) = < u cos v, u sin v, v > 0 <u<1, 0 < v < 2n 0 < u < 1, 0 sv< 2n with upward orientation.
Transcribed Image Text:Evaluate dS, where < y, – x, z³ > and S'is S the helicoid with vector equation r(и, v) = < u cos v, u sin v, v > 0 <u<1, 0 < v < 2n 0 < u < 1, 0 sv< 2n with upward orientation.
(y, 4+ 3x + y above the rectangle Find the flux of the vector field F z, x) across the part - of the plane z = 0, 4] x [0, 5] with upwards orientation.
Transcribed Image Text:(y, 4+ 3x + y above the rectangle Find the flux of the vector field F z, x) across the part - of the plane z = 0, 4] x [0, 5] with upwards orientation.
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