3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with clockwise orientation,
3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with clockwise orientation,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 3. This is Calculus 3
![where C is pomemetrized by r(t) = <t", t², +³>, 0£t≤).
Find a potential f for the vector field
F(x,y,z) =< sin (y), x· cos(y), - sin(z)).
C
3) Use Green's theorem to evaluate { x³y dx - xy²dy, where
C is the unit circle x² + y²=1 with clockwise onintation.
4 Use Stokes theorem to evaluate SF.dr, where
с
F(x,y,z) = < xy, yz, *x), where C is the triangle with vertices
(1,0,0), (0.1.0) (0.01)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41a1af84-f79e-495e-9bf6-e155c46aa5b8%2F56ffac92-071e-4a3a-8713-a2f5f4ff81c1%2Fg5hazz5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:where C is pomemetrized by r(t) = <t", t², +³>, 0£t≤).
Find a potential f for the vector field
F(x,y,z) =< sin (y), x· cos(y), - sin(z)).
C
3) Use Green's theorem to evaluate { x³y dx - xy²dy, where
C is the unit circle x² + y²=1 with clockwise onintation.
4 Use Stokes theorem to evaluate SF.dr, where
с
F(x,y,z) = < xy, yz, *x), where C is the triangle with vertices
(1,0,0), (0.1.0) (0.01)
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