The plane S can be parameterized by r(u, v) = (u, v, 3-u-2v with (u, v) E D, where D is bounded by u = 0, v = 0, and the line >

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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The plane S can be parameterized by ř(u, v) = (u, v, 3− u – 2v ✔ or )
with (u, v) € D, where D is bounded by u = 0, v = 0, and the line
Transcribed Image Text:The plane S can be parameterized by ř(u, v) = (u, v, 3− u – 2v ✔ or ) with (u, v) € D, where D is bounded by u = 0, v = 0, and the line
[[_curl(F) · ds = [[ curl(F(F(u, v))) · (Fu × Fv)dA, so we need to find curl (F) a
· and
Tu X Tv:
curl F
Tu × T v
Finally,
=
=
(1,2,-1)
(1,2,1)
OF
curl(F(F(u, v))) · (Fu × F„)dª
.
=
D
4
dA
=
Transcribed Image Text:[[_curl(F) · ds = [[ curl(F(F(u, v))) · (Fu × Fv)dA, so we need to find curl (F) a · and Tu X Tv: curl F Tu × T v Finally, = = (1,2,-1) (1,2,1) OF curl(F(F(u, v))) · (Fu × F„)dª . = D 4 dA =
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