# VC5.3

From Example Problems

By using Green's theorm, --(1)

Now,RHS of (1) =

= --(2)

We now evaluate the LHS of (1).

Along the line from O(0,0) to A(2,0),y=0,dy=0 and x varies from 0 to 2.

Along the line from A(2,0) to B(2,2),x=2,dx=0 and y varies from 0 to 2.

Along the line from B(2,2) to C(0,2),y=2,dy=0 and x varies from 2 to 0.

Along the line from C(0,2) to O(0,0),x=0,dx=0 and y varies from 2 to 0.

LHS =

=

=

= --(3)

Hence,from (2) and (3), LHS=RHS, So Green's theorm is verified.