Question 2

Let $\alpha = 2xydx - y^2dy$.
Calculate the line integral of $\alpha$ around the closed curve going first from the point $A = [4, 0]$ to the point $B = [0, 4]$ along the straight line $AB$ and then back to $A$ along the shorter arc $BA$ of the circle, with center the origin, that passes through $A$ and $B$.