The vector field $$\vec{F}(x,y)=(e^x-y)\vec{i} + (x-e^y)\vec{i}$$
goes goes around $(0,0)$, $(1,1)$, $(1,2)$, $ (0,3)$, $(-1,3)$, $(-2,2)$, $ (-2,1)$, $(-3,0)$ in order find the line integral.
How do I solve this question? Is there a easy way or should I use manual labor and split the segments?