Let F = (M,N) = (e, e) and D be the shaded region in the diagram...

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Let F = (M,N) = (e, e) and D be the shaded region in the diagram below. The left-side curve C is part of the parabola y = 1-x and the right-side curve C3 is part of the circle x + y = 1. Let C = C + C+ C3. (a) Use Green's theorem to show that 1 C2 1 I [1 mark] Md Mdx+Ndy 0 = = (b) Let Im Sc Mdx + Ndy. Evaluate I and 12. Note that [4 marks] Sted e-1 te- dt = 2e (c) Hence determine the value of 13. [1 mark] Let F = (M,N) = (e, e) and D be the shaded region in the diagram below. The left-side curve C is part of the parabola y = 1-x and the right-side curve C3 is part of the circle x + y = 1. Let C = C + C+ C3. (a) Use Green's theorem to show that 1 C2 1 I [1 mark] Md Mdx+Ndy 0 = = (b) Let Im Sc Mdx + Ndy. Evaluate I and 12. Note that [4 marks] Sted e-1 te- dt = 2e (c) Hence determine the value of 13. [1 mark]