Solution Verify Green's theorm in plane for where C is the region bounded by the parabolas
By Green's theorm,
Where R is the region bounded by .The bounding curve C is closed curve OAO where O is the origin and A(1,1).Now,on ,dy=2xdx and x varies from 0 to 1 and on dx=2ydy and y varies from 1 to 0.
= on simplification of the above.
= on simplification.
Therefore,LHS=RHS,hence the theorm is verified.