# Line integral of vector field whose curl=0

I've got a problem that's asking me to take the line integral of a conservative vector field, given by

V=xi+yj

I'm asked to perform the line integral using stoke's theorem for this field when a) the curve C is the unit circle in the xy plane centered at the origin, and b) when C is the same circle only centered at (1,0).

My thought was, since Stoke's theorem replaces F*dr in the integral with curl(F)*da, that the answer to both would be zero since curl(F)=0.

Does this make sense? I'm not sure since I'm asked to do a line integral of the same function twice.

Thanks!