(4) Consider the vector field F(x, y) = xyi - x²j (= F₁i + F₂j) and let C be the closed curve consisting of three segments: the straight line from (0,0) to (1,0) followed by the circular arc from (1, 0) to (0,1) followed by the straight line from (0, 1) to the origin (oriented anticlockwise). Let n denote the unit normal vector to C directed out of the region D bounded by C. (a) Calculate the line integral F. dr directly without using Green's theorem. √ F (b) Calculate the double integral JF2 მთ მყ OF₁ dA without using Green's theo- rem and compare your answer with part (a). (c) Calculate the flux out of D by evaluating the line integral $1 F n ds directly without using the flux form of Green's theorem. (d) Calculate the flux out of D by applying Green's Theorem and evaluating the double integral V.F dA.