Calculate the circulation of the vector field $\displaystyle F(x,y) = (x,xy)$ around the closed curve $\displaystyle x^2+y^2 = 25$ situated above the axis $\displaystyle OX$
we have talked before if F is a force field the line integral is the Work done
If F is a velocity field then the line integral is the circulation
so just compute the line integral of F over C
Her C consists of 2 parts the circle and the line segment along the x axis from -5 to 5
But of course you have Green's thm in your tool box as well