We are given the vector field $ x^2dx+y^2dy $ and are interested in the line integral of it over the closed equilateral triangle with vertices (0,0) (2,0) (1,-2)
Because the partial derivatives of each piece of this integral is 0, I thought I could use the Fundamental Theorem of Integrals but since it is a closed curve, I don't know if it would be easier to use Green's Theorem or maybe just evaluate each line of the curve separately.