- #1
taylormade
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Not exactly a homework problem, a problem from a sample test. I'm boning up for my qualifying exam.
Consider the vector field:
F = (ax + by)i + (cx + dy)j
where a, b, c, d are constants.
Let C be the circle of radius r centered at the origin and going around the origin one turn in the mathematically positive direction starting from the positive x-axis.
A parameterization for C is x = r cost y = r sint, (z=0), Where 0[tex] \leq [/tex] t [tex] \leq [/tex] 2 [tex] \pi [/tex]
Find the integral [tex] \int_{C}[/tex]F.dR for any values of a, b, c, d (the answer may depend on a, b, c, d)
The rust is killing me. I remember that I need line integrals to solve the problem, but the setup isn't coming out of the fog.
Homework Statement
Consider the vector field:
F = (ax + by)i + (cx + dy)j
where a, b, c, d are constants.
Let C be the circle of radius r centered at the origin and going around the origin one turn in the mathematically positive direction starting from the positive x-axis.
A parameterization for C is x = r cost y = r sint, (z=0), Where 0[tex] \leq [/tex] t [tex] \leq [/tex] 2 [tex] \pi [/tex]
Find the integral [tex] \int_{C}[/tex]F.dR for any values of a, b, c, d (the answer may depend on a, b, c, d)
Homework Equations
The Attempt at a Solution
The rust is killing me. I remember that I need line integrals to solve the problem, but the setup isn't coming out of the fog.