1. Consider the integral f v* dx – x* dy where C is the circle of radius 2 centered at the origin with positive orientation. (a) If F(æ, y) = (y°, –2*) then caleulate the quantity What does this make you think of? dy (b) Parameterize the boundary of the ellipse, making sure that your parameterization goes around once in a counter-clockwise direction. (c) Set up two equivalent integrals to calculate y* dx – a* dy. Choose one and evaluate it.
1. Consider the integral f v* dx – x* dy where C is the circle of radius 2 centered at the origin with positive orientation. (a) If F(æ, y) = (y°, –2*) then caleulate the quantity What does this make you think of? dy (b) Parameterize the boundary of the ellipse, making sure that your parameterization goes around once in a counter-clockwise direction. (c) Set up two equivalent integrals to calculate y* dx – a* dy. Choose one and evaluate it.
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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![1. Consider the integral
f y* dr – a* dy
where C is the circle of radius 2 centered at the origin with positive orientation.
(a) If F(xr, y) = (y°, –r*) then calculate the quantity
What does this make you think of?
(b) Parameterize the boundary of the ellipse, making sure that your parameterization goes around once
in a counter-clockwise direction.
(c) Set up two equivalent integrals to calculate o y³ dx – a³ dy. Choose one and evaluate it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F191441f0-66db-457d-b504-dd20fe1485fa%2Fbaf42af0-d88c-43b7-a8bc-3faac33f028c%2Fbxbwr2_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the integral
f y* dr – a* dy
where C is the circle of radius 2 centered at the origin with positive orientation.
(a) If F(xr, y) = (y°, –r*) then calculate the quantity
What does this make you think of?
(b) Parameterize the boundary of the ellipse, making sure that your parameterization goes around once
in a counter-clockwise direction.
(c) Set up two equivalent integrals to calculate o y³ dx – a³ dy. Choose one and evaluate it.
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