math192_hw9sp06 - HW9 Solutions 15.6 Triple Integrals in...

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Unformatted text preview: HW9 Solutions 15.6 Triple Integrals in Cylindrical and Spherical Coordinates 2 3 18-r 2 9 8 2 - 7 2. dzrdrd = 2 0 0 r 2 /3 1 2 0 0 1 0 0 2 cos cos /4 0 2 /4 0 /2 0 /4 0 /4 2 sec 0 sec 2 0 3-r sin r cos 1+cos 1 2 1 8. -1 /2 4rdrddz = -1 0 /2 2(1 + cos )2 ddz = -1 1 6d = 12 /2 14. -/2 /2 r3 dzdrd = -/2 0 r4 cos drd = 1 5 cos d = -/2 2 5 18. -/2 2 f (r, , z)dzrdr 22. 0 ( cos )2 sin ddd = 2 26. 0 3 sin cos ddd = 4 4 3 /4 /2 0 0 /4 52. V = 4 0 sec 2 sin ddd = sec3 sin dd = 28 3 /2 0 0 8 sec3 - sec3 sin dd 28 3 /2 0 28 3 14 = 3 = or /2 0 /2 0 tan sec2 dd = 1 tan2 2 /4 d 0 d = 0 7 3 2 2 1 0 z 2 2 1 V = 0 /2 rdrdzd = 0 2 1 0 2-r 2 z2 dzd = 2 4 3 2 0 z3 6 2 2 d = 1 0 7 7 d = 6 3 56. V = 8 0 dzrdrd = ...
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