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.
= [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.