Example 5.1.3
Let us compute the integral of the function
along two different paths.
First let
be the same path as in previous example. If
, then
. and we have:
Now we compute the integral of
along the segment from
to
on the
axis; a parametrization of the segment is given by
, for
. Thus we have:
Note that the two paths have the same origin and the same endpoint, but
the integrals are different. We will understand this phenomenon later (v.i.
Corollary
3.4).