4) Consider the magnetic field F = (cos(x) + 4xy, 2x² + sin(y)), and let R \text { be the boundary of the rectangle: } 0 \leq x \leq 3,0 \leq y \leq 2 a) Show that F is conservative. b) Explain why (or show that) the counterclockwise circulation of F around R starting and ending at (0, 0) is 0. c) Compute the outward flux of F across R. Show all work.