Find the work done by the force $e^y{\bf i}+xe^y {\bf j}$ along the unit circle $x^2+y^2=1$ traversed once counterclockwise from (1, 0)(1,0) back to (1, 0)(1,0).
I got this down to the integral from 0 to 2pi of e^sint(cos^2(t) - sint)dt but this seems uncomputable. Is there another way to do this with another theorem?