![]() ![]() |
Let
be a function continuous at every point of
.
Then
and
. we have:
![]() |
![]() |
|
![]() |
![]() |
|
![]() |
![]() |
|
![]() |
![]() |
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).
Noah Dana-Picard 2007-12-24