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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
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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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)
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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