Consider the vector field shown below.
(Note: For the vector field, vectors are shown with a
dot at the tail of the vector.)
Let be the line from to
,
be the line from to
, and
be the semi-circle centered on the origin that goes from
to
in a counterclockwise direction.
Is the line integral of the vector field along each of these curves positive,
negative or zero?
Along , the integral is
Along , the integral is
Along , the integral is
You can earn partial credit on this problem.