Evaluate the line integral of F dot dr by evaluating the surface integral in Stokes' Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.
F = (y2, - z2, x); C is the circle r(t) = < 3cos(t), 4cos(t), 5sin(t) >
F[/B] is the vector field.
The Attempt at a Solution
I found the curl of F to be <2z, -1, -2y> and I computed the line integral and got 15pi, which is the correct solution, but I have to use Stokes' Theorem to arrive at that solution. My main problem is I have no clue how to solve for the normal vector to dot with the curl of F. The main thing throwing me off is that C is already parameterized and I cannot see how to un-parameterize it to get the equation for the circle out.
Thank you in advance.