Consider the curve C1 consisting of the straight line from (1, 0) to (−1, 0), and the curve C2 consisting of the arc of circle from (1, 0) to (−1, 0), in the counterclockwise direction.

Consider the curve C1 consisting of the straight line from (1, 0) to (−1, 0), and the curve
C2 consisting of the arc of circle from (1, 0) to (−1, 0), in the counterclockwise direction.

1. Compute
   Z
   C1
   e
   x
   dx + x dy, Z
   C2
   e
   x
   dx + x dy.
2. Compute
   Z
   C1
   (1 + y) dx + (x + 2y) dy, Z
   C2
   (1 + y) dx + (x + 2y) dy.
3. What do you notice?