hwsol_23

# hwsol_23 - Homework Assignment 23 - (13.6)-(13.7) -...

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Homework Assignment 23 - (13.6)-(13.7) - Solutions Page 1070 : 8*, 12*, 16*, 18*, 22*, 26*, 30*, 38*, 42* Page 1077: 12*, 18*, 20*, 22*,27*, 28*, 34*, 38*, 44*, 54*, 58* Page 1070 : 8. x 2 ! ! y ! 3 " 2 " 9 # x 2 ! y 2 ! 6 y ! 9 " 9, x 2 ! y 2 " 6 y r 2 " 6 r sin ! # r " 6sin ! 12. z " e ! x 2 ! y 2 , z " e ! r 2 16. Q : x 2 ! y 2 " z " 4 ! x 2 ! y 2 # r " z " 4 ! r 2 Intersection: x 2 ! y 2 " 4 ! x 2 ! y 2 ,2 ! x 2 ! y 2 " " 4, x 2 ! y 2 " 2, R : x 2 ! y 2 " 2 Q : r " z " 4 ! r 2 ,0 " r " 2 " ! " 2 " ### Q f ! x , y , z " dV " # 0 2 " # 0 2 # r 4 ! r 2 f r cos ! , r sin ! , z rdzdrd ! 18. Q :above the xy ! plane and below z " 4 ! x 2 ! y 2 in the first octant. When z " 0, 4 ! x 2 ! y 2 " 0 # R : x 2 ! y 2 " 4 Q :0 " z " 4 ! r 2 " r " 2, 0 " ! " " 2 Q f ! x , y , z " dV " # 0 " /2 # 0 2 # r 4 ! r 2 f r cos ! , r sin ! , z rdzdrd ! 22. Q :bounded by y " x 2 ! z 2 and y " 9 When y " 9, x 2 ! z 2 " 81 # R : x 2 ! z 2 " 81 Q : r " y " 9, R " r " 9, 0 " ! " 2 " Q f ! x , y , z " dV " # 0 2 " # 0 9 # r 9 f r cos ! , r sin ! , z rdydrd ! 26. Q : x 2 ! y 2 " 4, between z " 0 and z " 3 Q " z " 3, 0 " r " 2, 0 " ! " 2 " Q ze x 2 ! y 2 dV " # 0 2 " # 0 2 # 0 3 ze r rdzdrd ! " 9 e 2 " ! 9 " " 237. 20 30. Q :between z " x 2 ! y 2 , z " 0 and inside x 2 ! y 2 " 4. Q " z " r " r " 2, 0 " ! " 2 " # 0 2 " # 0 2 # 0 r r 2 dzdrd ! " 8 " " 25. 13274 38. 1

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# 0 1 # ! 1 ! x 2 1 ! x 2 # 0 2 ! x 2 ! y 2 x 2 ! y 2 dzdydz " # ! " /2 " /2 # 0 1 # 0 2 ! r 2 r 2 dzdrd ! " 7 15 " " 1. 466077 42. # ! 2 2 # ! 4 ! z 2 4 ! z 2 # y 2 ! z 2 4 ! y 2 ! z 2 " 3/2 dxdydz " # 0 2 " # 0 2 # r 2 4 r 4 dxdrd ! " 512 35 " " 45. 95701 Page 1077: 12*, 18*, 20*, 22*,27*, 28*, 34*, 38*, 44*, 54*, 58* 12. 2 , " 4 , " 3 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_23 - Homework Assignment 23 - (13.6)-(13.7) -...

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