Find the k-component of (curl F) for the following vector field on the plane. F = (x + y)i + (3xy)j (curl F). k= ...

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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Find the k-component of (curl F) for the following vector field on the plane.
F = (x + y)i + (3xy)j
(curl F). k=
Transcribed Image Text:Find the k-component of (curl F) for the following vector field on the plane. F = (x + y)i + (3xy)j (curl F). k=
Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the
field F = - 3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C:
r = (a cost)i + (a sin t)j, 0≤t≤ 2.
Click the icon to view the two forms of Green's Theorem.
The flux is
(Type an exact answer, using as needed.)
The circulation is
(Type an exact answer, using as needed.)
Transcribed Image Text:Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of Green's Theorem for the field F = - 3yi + 3xj. Take the domains of integration in each case to be the disk R: x² + y² ≤a² and its bounding circle C: r = (a cost)i + (a sin t)j, 0≤t≤ 2. Click the icon to view the two forms of Green's Theorem. The flux is (Type an exact answer, using as needed.) The circulation is (Type an exact answer, using as needed.)
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