C is the path from P to Q in the figure below that traces C1, C2 and C3 in the orientation indicated, and F is a vector field such that
Find the value of , where C' is the path that traverses the loop C2 3 times in the clockwise direction.
Since C' is the path that traverses the loop C2 3 times in the clockwise direction, the line integral
is times the line integral
Thus we need to calculate .
Using additivity and reversing orientation of vector line integrals, calculate .
= ()
=
Thus = .
Calculate .