Line Integral over Vector Field?

[taylormade]

Not exactly a homework problem, a problem from a sample test. I'm boning up for my qualifying exam.

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\leq t \leq 2 \pi

Find the integral \int_{C}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.

 

[Dick]

In terms of your parametrization C, dR is (-r*sin(t)dt,r*cos(t)dt). Do you see why? Now express the vector F in terms of t and take the dot product. You'll wind up with two integrals dt to do. Any clearer?