Let a: DR³ be the parametric surface defined by D= {(u, v) ER² | ue [0, 1], v € [0, z]} and a(u, v) = (u cos(v), u sin(v), v). (This is know as an "helicoid".) Let @= y dy Adz + 5z dx Ady be a two-form on R³. Evaluate the surface integral of @ along a. 1.0= a
Let a: DR³ be the parametric surface defined by D= {(u, v) ER² | ue [0, 1], v € [0, z]} and a(u, v) = (u cos(v), u sin(v), v). (This is know as an "helicoid".) Let @= y dy Adz + 5z dx Ady be a two-form on R³. Evaluate the surface integral of @ along a. 1.0= a
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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![Let a: DR³ be the parametric surface defined by
D= {(u, v) ER² | ue [0, 1], v € [0, z]} and
a(u, v) = (u cos(v), u sin(v), v).
(This is know as an "helicoid".) Let @ = y dydz + 5z dx Ady be a two-form on R³.
Evaluate the surface integral of w along a.
1. Ⓡ =
a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb126cdff-8dab-4db7-a7f7-87720b301f49%2F31622c3d-70be-4dac-81f5-82601603e4b7%2Flektx35_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a: DR³ be the parametric surface defined by
D= {(u, v) ER² | ue [0, 1], v € [0, z]} and
a(u, v) = (u cos(v), u sin(v), v).
(This is know as an "helicoid".) Let @ = y dydz + 5z dx Ady be a two-form on R³.
Evaluate the surface integral of w along a.
1. Ⓡ =
a
![Evaluate the integral of the two-form w = 3xe-3xy dx A dy over the region
D = {(x, y) E R² | x € [1,7], y = [0, 1]}
with canonical orientation.
1₁0 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb126cdff-8dab-4db7-a7f7-87720b301f49%2F31622c3d-70be-4dac-81f5-82601603e4b7%2Fxtjec7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the integral of the two-form w = 3xe-3xy dx A dy over the region
D = {(x, y) E R² | x € [1,7], y = [0, 1]}
with canonical orientation.
1₁0 =
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