1. Let F = (M, N) = (3e, 2e) and D be the shaded region in...

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1. Let F = (M, N) = (3e, 2e) and D be the shaded region in the diagram below. The left-side curve C is part of the curve y = 126 and the right-side curve C3 is part of the curve x + y = 1. Let C = C + C+ C3. C C3 I 1 C2 (a) Use Green's theorem to show that [1 mark] M Mdx+Ndy = 0 = (b) Let Im Sc Mdx + Ndy. Evaluate I and 12. Note that [4 marks] e-1 t5e-to dt = 6e (c) Hence determine the value of 13. [1 mark] 1. Let F = (M, N) = (3e, 2e) and D be the shaded region in the diagram below. The left-side curve C is part of the curve y = 126 and the right-side curve C3 is part of the curve x + y = 1. Let C = C + C+ C3. C C3 I 1 C2 (a) Use Green's theorem to show that [1 mark] M Mdx+Ndy = 0 = (b) Let Im Sc Mdx + Ndy. Evaluate I and 12. Note that [4 marks] e-1 t5e-to dt = 6e (c) Hence determine the value of 13. [1 mark]