Let C be the curve consisting of the three line segments from (0,0) to (1, 1), from (1, 1) to (1, -1), and from (1,-1) to (0,0). Use Green's theorem to find the flux integral of F = x²i+x²j across C. Let C₁ be the curve that starts at (1, 1), ends at (0,0), and has the parameterization r(t) = (1 − t, 1 − t), where t = [0, 1]. Let C₂ be the curve that starts at (1,1), ends at (0,0), and has the parameterization r(t) = (1+ cost, sint), where t Є [½‚π]. An unknown vector field F satisfies curl(F) = x + y and set up a double integral equal to the circulation integral C₁ F.dr = 0. Use Green's theorem to F dr. Do not evaluate. C2

Let C be the curve consisting of the three line segments from (0, 0) to (1, 1), from (1, 1) to (1, −1), and from (1, −1) to (0, 0).                                                                                                                                                                                                                                                                                                                                                           Use Green’s theorem to find the flux integral of F = x^2i + x^2j across C.
                                                                                                                                                                                                                                                                                                                                                                                Let C1 be the curve that starts at (1, 1), ends at (0, 0), and has the parameterization r(t) = (1 − t, 1 − t), where t ∈ [0, 1]. Let C2 be the curve that starts at (1, 1), ends at (0, 0), and has the parameterization r(t) = (1 + cost, sin t), where t ∈ [π/2, π].
                                                                                                                                                                                    An unknown vector field F satisfies curl(F) = x + y and Z C1 F · dr = 0. Use Green’s theorem to set up a double integral equal to the circulation integral Z C2 F · dr. Do not evaluate.