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 $t times in the clockwise direction.
Since C' is the path that traverses the loop C2 $t times in the clockwise direction, the line integral
is P/b5D6yaZJc= times the line integral
Thus we need to calculate .
Using additivity and reversing orientation of vector line integrals, calculate .
= (UYinCekNO0E=)
9DxysKU6P+4= 9DxysKU6P+4=
= U2GIbglD1oM=
Thus = 5dWJhLEUU4Y=.
Calculate .
or6dmYWrEbA=