Problem 7. Consider the line integral Z C y sin x dx − cos x dy.
(Please show all work)
a. Evaluate the line integral, assuming C is the line segment
from (0, 1) to (π, −1).
b. Show that the vector field F = is conservative, and find a
potential function V (x, y).
c. Evaluate the line integral where C is any path from (π, −1)
to (0, 1).