Consider the vector field F=-yi+xj. (a) Is F conservative? Explain briefly. (b) Let C₁ be the closed path that starts at the origin, heads to (2, 4) along the curve y = 2² and then heads back to the origin in a straight line. Evaluate the path integral of F along C₁, that is: SOF F.dr. You may either do it directly (parametrize C₁ etc) or use Green's theorem to turn it into a double integral and then evaluate that.