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hwsol_20

# hwsol_20 - Homework Assignment 20(13.3 Solutions Page 1045...

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Homework Assignment 20 - (13.3) - Solutions Page 1045 : 6*, 9* - also sketch the graph for each problem 14*, 18*, 22* - without using a calculator 25*, 26*, 28*, 31* , 35*, 37* 6. r ! 2 ! 2cos ! ! r 0 0 " 2 2 " 4 3 " 2 2 2 " 0 -2 -1 0 1 2 -4 -3 -2 -1 A ! " 0 2 " " 0 2 ! 2cos ! rdrd ! ! " 0 2 " 1 2 r 2 | 0 2 ! 2cos ! d ! ! 1 2 " 0 2 " ! 2 ! 2cos ! " 2 d ! ! 2 " 0 2 " ! 1 ! 2cos " cos 2 ! " d ! ! 2 " 0 2 " 1 ! 2cos " 1 2 ! 1 " cos ! 2 ! "" d ! ! 2 ! ! 2sin ! " 1 2 ! " 1 4 sin ! 2 ! " 0 2 " ! 2 3 2 ! 2 " " ! 6 " ! 18. 84956 9. r ! sin ! 3 ! " , for one leaf: sin ! 3 ! " ! 0 # ! ! 0 and ! ! " 3 ! r ! r 0 0 2 " 9 3 2 " 18 1 2 " 4 1 2 " 12 1 2 " 3 0 " 9 3 2 " 6 1 0 0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 A ! " 0 " /3 " 0 sin ! 3 ! " rdrd ! ! " 0 " /3 1 2 sin 2 ! 3 ! " d ! ! 1 4 " 0 " /3 ! 1 ! cos ! 6 ! "" d ! ! 1 4 ! ! 1 6 sin ! 6 ! " 0 " /3 ! 1 4 " 3 ! " 12 ! 0.2617994 14. R : x 2 " y 2 # 16 # R : 0 # ! # 2 " , 0 # r # 4 1

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"" R x 2 " y 2 " 1 dA ! " 0 2 " " 0 4 1 " r 2 rdrd ! u ! 1 " r 2 , du ! 2 rdr ! ! 2 " " " 1 17 u 1 2 du ! " 2 3 u 3/2 1 17 ! 2 " 3 ! 17 3/2 ! 1 " ! 144. 7076 18. R : r ! 1 ! sin ! # 0 # r # 1 ! sin ! , 0 # ! # 2 " "" R xdA ! " 0 2 " " 0 1 ! sin ! r 2 cos ! drd ! ! " 0 2 " 1 3 r 3 cos ! | 0 1 ! sin ! d ! ! 1 3 " 0 2 " ! 1 ! sin ! " 3 cos ! d ! u ! 1 ! sin ! , du ! ! cos ! d ! ! 1 3 " 1 1 u 3 ! ! du " ! 0 22. R : x 2 " y 2 # 9 # 0 # ! # 2 " , 0 # r # 3 "" R cos x 2 " y 2 dA ! " 0 2 " " 0 3 cos ! r " rdrd ! u ! r , dv ! cos r ! 2 " ! r sin r " cos r " | 0 3 ! 2 " ! 3sin3 " cos3 ! 1 " ! ! 9. 843442 25. The solid: 0 # z # x 2 " y 2 , R : x 2 " y 2 # 4 # 0 # z # r , R : 0 # ! # 2 " , 0 # r # 2 V ! " 0 2 " " 0 2 r 2 drd ! ! 16 3 " ! 16. 75516 26. The solid: 0 # z # x 2 " y 2 , R : x 2 " ! y ! 1 " 2 # 1 x 2 " ! y ! 1 " 2 ! 1 # x 2 " y 2 ! 2 y ! 0 # r 2 ! 2 r sin ! # r ! 2sin ! The solid: 0 # z # r , R : 0 # ! # " , 0 # r # 2sin ! V ! " 0 " " 0 2sin ! r 2 drd ! ! 32 9 28. The solid: 0 # z # 8 ! x 2 ! y 2 , R : x 2 " y 2 # 8 # 0 # z # 8 ! r 2 , R : 0 # ! # 2 " , 0 # r # 2 2 V ! " 0 2 " " 0 2 2 ! 8 ! r 2 " rdrd ! ! 32 " 31. The solid: 0 # z # 4 ! x 2 ! y 2 , R : 0 # y # x and x 2 " y 2 # 4 The intersection of y ! x and x 2 " y 2 ! 4 : 2 x 2 ! 4, x 2 ! 2, x ! # 2 -2 -1 0 1 2 -2 -1 1 2 t 2
The solid: 0 # z # 4 ! r 2 , R : 0 # ! # " 4 , 0 # r # 2 V ! " 0 " /4 " 0 2 ! 4 ! r 2 " rdrd ! ! " 35. " 0 2 " ! 4 ! x 2 4 ! x 2 e ! x 2 ! y 2 dydx ! " ! " /2 " /2 " 0 2 e ! r 2 rdrd ! ! ! 1 2 e ! 4 " " 1 2 " ! 1. 542026 37. " 0 2 " x 8 ! x 2 !
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