Show that the given integral is independent of the path.

F(x,y) = (2xy)dx + (x^2)dy

So i take the integral of 2xy w.r.t x and it gives:

x^2*y + g(y)

now I take the partial derivative of that function w.r.t to y and i get:

x^2 + g'(y)

I set it equal to (x^2)

so

x^2 + g'(y) = x^2

so g'(y) = 0

so i would integrate

x^2*y + 0

is that right?

Thank you