hwsol_18

hwsol_18 - Homework Assignment 19(13.2 Solutions Page 1037...

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Homework Assignment 19 - (13.2) - Solutions Page 1037: 12*, 14*, 20*, Sketch first the solid for each problem. 28*, 30*, 34*, 35*, 42*, 51* 6. f ! x , y " ! 4 x 2 " y ,1 ! x ! 5, 0 ! y ! 2, n ! 2 # x ! 5 " 1 2 ! 2, # y ! 2 " 0 2 ! 1, $ x i % ! 1, 3, 5 , y i ! 0, 1, 2 Midpoints: 2, 1 2 , 4, 1 2 , 2, 3 2 , 4, 3 2 V # f 2, 1 2 " f 4, 1 2 " f 2, 3 2 " f 4, 3 2 ! 2 "! 1 " ! 4 ! 2 " 2 " 1 2 " 4 ! 4 " 2 " 1 2 " 4 ! 2 " 2 " 3 2 " 4 ! 4 " 2 " 3 2 ! 2 " ! 328 14. $$ R ! 2 xy " y 3 " dA ! $ " 1 2 $ 0 2 ! 2 xy " y 3 " dydx ! $ " 1 2 xy 2 " 1 4 y 4 0 2 dx ! $ " 1 2 x ! 4 " " 1 4 ! 16 " 0 2 dx ! ! 2 x 2 " 4 x " " 1 2 ! 2 ! 4 " 1 " " 4 ! 2 " ! " 1 "" ! 18 18. R 3 x " 4 xx y dA ! $ 0 4 $ 0 9 ! 3 x " 4 x 3/2 y 1/2 " dydx ! $ 0 4 3 xy " 8 3 x 3/2 y 3/2 0 9 dx ! $ 0 4 ! 27 x " 72 x 3/2 " dx ! 27 2 x 2 " 72 2 5 x 5/2 0 4 ! 27 2 ! 16 " " 144 5 ! 32 " ! " 3528 5 22. $ " 1 1 $ " 1 1 ! 4 " x 2 " y 2 " dydx The solid: 0 ! z ! 4 " x 2 " y 2 , " 1 ! y ! 1, " 1 ! x ! 1 When x ! 1, and y ! 1, f ! x , y " ! 4 " 2 ! 2 0 1 2 3 4 -4 -2 2 4 v -4 -2 2 4 u 26. 1
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$ " 2 2 $ 0 y ! x 3 " 1 " dxdy ! $ " 2 2 1 4 x 4 " x 0 y dy ! $ " 2 2 1 4 y 4 " y dy ! 2 $ 0 2 1 4 dy " 0 ! 1 10 y 5 0 2 ! 1 10 ! 32 " ! 16 5 ! 3.2 30. $ 1 2 $ 0 2/ x e xy dydx ! $ 1 2 1 x e xy | 0 2/ x dx ! $ 1 2 1 x ! e 2 " 1 " dx ! ! e 2 " 1 " ln| x | 1 2 ! ! e 2 " 1 " ln ! 2 " ! 4. 428556 31. $ 1 4 $ 0 1/ x cos ! xy " dydx ! $ 1 4 1 x sin ! xy " | 0 1/ x dx ! $ 1 4 1 x ! sin ! 1 " " 0 " dx ! sin ! 1 " ln| x | 1 4 ! sin ! 1 " ln ! 4 " ! 1. 166526 36. z ! 3 x 2 " 2 y , z ! 0, y ! 0, y ! 1, x ! 1, x ! 3 The solid region: 0 ! z ! 3 x 2 " 2 y ,0 ! y ! 1, 1 ! x ! 3 V !
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This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.

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hwsol_18 - Homework Assignment 19(13.2 Solutions Page 1037...

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