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Written homework problem 17 Assigned 11/5 and due 11/10 (Variation on problem 2 from the spring 2011 take-home exam 3.) Evaluate Z π/2 dt p . 2 sin(t) cos(t)(sin(t) + cos(t)) 0 [ Warning: I think if you plug this into Maple, Maple will give you the wrong answer. Here are some hints. ] I= y x 4 4 (a) Let F~ (x, y) = h− x2 +y = 1 in the 1st 2 , x2 +y 2 i. Let C1 be the part of the curve x + y quadrant, p so the start point is (1, 0) and the end p oriented R point is (0, 1). Parametrize C1 by ~r(t) = h cos(t), sin(t)i, 0 ≤ t ≤ π/2. Show that I = C1 F~ · d~r. (b) Let C2 be the part of the unit circle in the 1st quadrant, oriented so the start point is (1, 0) and the end point is (0, 1). Evaluate Z F~ · d~r. C2 (c) Explain why R C1 F~ · d~r = R C2 F~ · d~r. 1