Show that this line integral is independent of path and then evaluate?

Question

∫_(-1,2)^(3,1) (y^2+2xy) dx + (x^2+2xy) dy

Answer 1

I have to say I never touched these... however contour integrals are starting to pop up in my graduate course, heh.

See below for some links which might help:

Answer 2

Your differential form is exact meaning you have the partial derivatives of a function. To check that you differentiate the first function with respect to y and the secund with respect to x . You get the same that is 2y+2x. So there is a function F(x,y) =xy(x+y) such that and so on and so forth.