Consider the curve C consisting of the graph of y = e

Consider the curve C consisting of the graph of y = e
x
for x ∈ [0, 3]. Compute
Z
C
e
2x
ds
and
Z
C
xy dx + e
−x
dy.

2. Consider the curve C consisting of the straight line from (0, 0) to (1, 0), then from
   (1, 0) to (0, 1) along the circle of radius 1 around the origin (in the counterclockwise
   direction), and finally the straight line from (0, 1) to (1, 0). Compute
   Z
   C
   x
   2
   dx + x dy.