Now for this implies
Taking the partial integral of both sides with respect to x gives
Since we know what the partial with respect to is we can determine the function
This implies that
So the potential function is
For Part B:
Since has a potential function the fundamental theorem of lines integrals applies and the integral is
Now for if you try to mimic the process you will find that you cannot find a potential function (the arbitary function of integration will is a function of one variable, but you will find that it is not!
Because of this the linear integral must be evaluated directly. Since it is a circular arc parametrize it with polar coordinates.