An equation is exact if it has a potential function e.g there is a scalar function such that with

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.