FM5002-HW5-2.22.12

B from problem 0042 4 we have that d 6 r r d c by

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Unformatted text preview: (1). Let b = Β (0) = Α (1). Let c = Γ (0) = Β (1). Let d = ∆ (0) = Γ (1). Let K be the 1 − chain {(a, b), (b, c), (c, d), (d, a)}. Define f : by f x y P Q. Note that f z z 2. Let Ω P dx Q dy. Ω. Compute K Ω K d x2 dΩ a , b x c ,d y2 dx 2 xy dy 2 y dy dx a , b x c ,d 2 y dx dy a , b x c ,d 0 0. a , b x c ,d 0042− . 7 Let P p x, y x2 y2. Let Q q x, y 2 x y. Let Α (t) = 5 + (3 + t) , Β (t) = (5 −3 t) + 4 , Γ (t) = 2 + (4 − t) , ∆ (t) = (2 +3 t) + 3 , for 0 <= t <= 1. Let a = Α (0) = ∆ (1). Let b = Β (0) = Α (1). Let c = Γ (0) = Β (1). Let d = ∆ (0) = Γ (1). Let K be the 1 − chain {(a, b), (b, c), (c, d), (d, a)}. Compute P Q dx dy . That is, compute K P dx K Q dy K P dx K Q dx K P dy K Q dy K dP dx a , b x c ,d Q dx K P dy. K dQ dy a , b x c ,d dQ dx a , b x c ,d dP dy a , b x c ,d FM5002−HW5−2.22.12.nb 2 y dy dx 2 y dx dy a , b x c ,d 2 x dy dx a , b x c ,d 9 ,8,7 0042 8. Compute x dx x y 2 x dx dy a , b x c ,d x2 dy z 5 0. a , b x c ,d dz. That is, compute x dx 7 ,8,9 y x x2 dy z dz, L where L is the directed line segment from 7, 8, 9 to 9, 8, 7 . We use the parametrization x t 7 2 t, y t 9 ,8,7 an d z t 9...
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This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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