Module 16 : Line Integrals, Conservative fields Green's Theorem and applications
Lecture 47 : Fundamental Theorems of Calculus for Line integrals [Section 47.1]
Then, the points cannot be joined by any continuous path completely lying inside . To go from the point to the point , one has to cross the annulus region.
Practice Exercises
(1)
For the following show that , for sum . Use this to compute for the given :
(i)
, is the line segment joining with .
(ii)
, is the semi-circular path in the upper half -plane joining to
cannot be joined by any continuous path 
completely lying inside 
. To go from the point 
to the point 
, one has to cross the annulus region. 
, for sum 
. Use this to compute 
for the given 
: 
, 
is the line segment joining 
with 
. 
, 
is the semi-circular path in the upper half 
-plane joining 
to 
around the 
traced in the counter clockwise direction.
) 
such that the vector-field 
has a potential function.
