hwsol_27

hwsol_27 - Homework Assignment 27 - (14.4) - Solutions Page...

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Homework Assignment 27 - (14.4) - Solutions Page 1142: 5*, 7*, 11*, 13*, 15*, 17*, 38*, 39(extra points) 5. ! C ! x 2 " y " dx ! y 2 dy , C : x 2 ! y 2 " 1, counterclockwise a. r # ! t " "$ cos t , sin t % ,0 # t # 2 ! , r # ! t " "$ " sin t , cos t % ! C ! x 2 " y " dx ! y 2 dy " $ 0 2 ! $ cos 2 t " sin t , sin 2 t % # $ " sin t , cos t % dt " $ 0 2 ! " sin t cos 2 t ! sin 2 t ! cos t sin 2 t dt " ! b. F 1 ! x , y " " x 2 " y , F 2 ! x , y " " y 2 , R : x 2 ! y 2 # 1 % F 1 % y " " 1, % F 2 % x " 0 ! C ! x 2 " y " dx ! y 2 dy " $ 0 2 ! $ 0 1 ! 0 " ! " 1 "" rdrd " " ! 7. ! C x 2 dx " x 3 dy , C : a square from ! 0,0 " to ! 0,2 " to ! 2,2 " to ! 2,0 " to ! 0,0 " a. C " C 1 C 2 C 3 C 4 C 1 : from ! 0,0 " to ! 0,2 " , x " 0, dx " 0, 0 # y # 2 C 2 : from ! 0,2 " to ! 2,2 " , y " 2, dy " 0, 0 # x # 2 C 3 : from ! 2,2 " to ! 2,0 " , x " 2, dx " 0, y is from 2 to 0 C 4 : from ! 2,0 " to ! 0,0 " , y " 0, dy " 0, x is from 2 to 0 F # ! x , y " "$ x 2 , " x 3 % ! C x 2 dx " x 3 dy " $ C 1 x 2 dx " x 3 dy ! $ C 2 x 2 dx " x 3 dy ! $ C 3 x 2 dx " x 3 dy ! $ C 4 x 2 dx " x 3 dy " $ 0 2 0 ! $ 0 2 x 2 dx " 0 ! $ 2 0 ! 0 " 8 " dy ! $ 2 0 x 2 dx " 0 " 1 3 x 3 | 0 2 " 8 y | 2 0 ! 1 3 x 3 | 2 0 " 16 b. F 1 ! x , y " " x 2 , F 2 ! x
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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_27 - Homework Assignment 27 - (14.4) - Solutions Page...

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