# VC5.7

From Example Problems

Here the parabola and the straight line x=2 intersect at the point say A(2,4) and B(2,-4). Thus the closed curve C consists of straight line BA and AOB of the parabola . Let R be the region bounded by C. Then,by Green's theorm in plane,we have

RHS of (1) =

= on integrating w.r.t. y.

=

= --(2)

Now,LHS=

=

=

= [Note that and are respectively odd and even function of y]

=

= on simplification. --(3)

From (2) and (3) LHS = RHS,hence Green's theorm is verified.