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**1. The problem statement, all variables and given/known data**

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)

**2. Relevant equations**

**3. 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.