# VC5.12

From Example Problems

**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.

LHS=

=

= on simplification of the above.

Again,RHS=

=

= on simplification.

Therefore,LHS=RHS,hence the theorm is verified.