old quiz 4 - Math 2401 Quiz 4 Solutions Open Book and Notes...

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Unformatted text preview: Math 2401 Quiz 4 Solutions April 12 2007 Open Book and Notes. Carefully explain your proceedures and answers. Calculators allowed, but answers mush be exact. Problem 1 (9 points) George Mallory needs to know the following : Let R be the conical right cylindrical region, with apex at 0, 0, 0 , and axis along the z axis, with height 2 and radius 1. Set up the integral in spherical coordinates : : xi R yj y2 z z 4 4k xyz 2 32 x2 Ans x y z Ρ cos Θ sin Ρ sin Θ sin Ρ cos 0 arctan 1 2 30 degress Π6 dxdydz 2Π 0 0 Ρ sin 2 dΡdΘd 0 2 cos Ρ cos Θ sin 0 i Ρ sin Θ sin j 2 Ρ cos Ρ sin 4k Θ sin 2 Ρ cos Θ sin Ρ cos 4 2 32 Ρ Θ Math 2401 Quiz 4 Solutions April 12 2007 Problem 2 (9 points) Set up the line integral C xy3 dx - xy dy a) Where C is the curve from (2,0) to (-2,0) given by: 2 quiz4ans.nb Along C1 : x Along C2 : x Along C3 : x 1 2 2, y t, t goes from 0 to 1 t, y 1, t goes from 2 to 2 2, y t, t goes from 1 to 0 0 2t t 0 2 t^3 t 1 1t t b) Where C is the curve from (2,0) to (-2,0) given by: Along C1 x Along C2 : x Π 12 cos Θ , y sin Θ , goes from 0 to t, y 0, t goes from 0 to 2 12 12 cos Θ cos Θ sin Θ ^ 3 sin Θ Θ Θ Π sin Θ 0 Π cos Θ 0 2 0t 0 Math 2401 Quiz 4 Solutions April 12 2007 Problem 3 (10 points) Consider the integral: limites) 3 3 3 31 ex 2 y2 2 3xy x y. Make a change of variables u = x+y, v = x-y, and set up the resultant integral (with Ans Clear u, v, x, y x, y u 2 D x, u 1 2 D x, v 1 2 D y, u 1 2 v , 2 u x, y v . Solve u x y, v x y, x, y 1 quiz4ans.nb 3 D y, v 1 2 J 1 2 ? ? ? ? Det D x, u , D y, u , D x, v , D y, v e 1 uv 1 v u 3 6v 2 Region in u, v space is a diamond : This gives the limits as : 0 u6 e 1 uv 1 v u 3 6 0 6u 6u e 1 uv 1 v u 3 6 u6 6v 2 6v 2 ...
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This note was uploaded on 06/07/2009 for the course MATH 2401 taught by Professor Morley during the Spring '08 term at Georgia Tech.

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old quiz 4 - Math 2401 Quiz 4 Solutions Open Book and Notes...

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