Here the integration is performed in the xy-plane.
Now,by defintion,the circulation of F round C =
where denote straight lines OP,PQ,QR and RO respectively.
Now,on C1,y=0,dy=0 and x varies from 0 to 1,therefore, --(1)
Next,on C2,x=1,dx=0 and y varies from 0 to ,therefore,
Again on C3,,dy=0 and x varies from 1 to 0.
Finally,on C4,x=0,dx=0 and y varies from to 0.
Using (1),(2),(3) and (4),