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Pre-Calc Homework Solutions 404

Pre-Calc Homework Solutions 404 - 404 30 y so Section 10.1...

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30. y 5 0 for t 5 0 and t 5 2 p . x 9 5 a 2 a cos t , y 9 5 a sin t , so Area 5 E 2 p 0 2 p [ a (1 2 cos t )] ˇ ( a w 2 w a w c w o w s w t ) w 2 w 1 w ( w a w s w in w t w ) 2 w dt 5 2 p a 2 E 2 p 0 (1 2 cos t ) ˇ 2 w 2 w 2 w c w o w s w t w dt 5 2 p a 2 E 2 p 0 1 2 sin 2 1 } 2 t } 22 ! 4 § s § in § 2 § 1 } § 2 t } § 2 § dt 5 8 p a 2 E 2 p 0 sin 3 1 } 2 t } 2 dt 5 8 p a 2 E 2 p 0 1 1 2 cos 2 1 } 2 t } 22 sin 1 } 2 t } 2 dt 5 8 p a 2 3 2 2 cos 1 } 2 t } 2 1 } 2 3 } cos 3 1 } 2 t } 24 5 } 64 p 3 a 2 } 31. } d d x t } 5 a (1 2 cos t ) (Note: integrate with respect to x from 0 to 2 a p ; integrate with respect to t from 0 to 2 p .) Area 5 E 2 a p 0 y dx 5 E 2 a p 0 a (1 2 cos t ) a (1 2 cos t ) dt 5 a 2 E 2 p 0 (1 2 2 cos t 1 cos 2 t ) dt 5 a 2 3 t 2 2 sin t 1 } 2 t } 1 } 1 4 } sin 2 t 4 5 3 p a 2 32. } d d x t } 5 a (1 2 cos t ), so Volume 5 E 2 p 0 p [ a (1 2 cos t )] 2 a (1 2 cos t ) dt 5 p a 3 E 2 p 0 (1 2 3 cos t 1 3 cos 2 t 2 cos 3 t ) dt 5 p a 3 3 t 2 3 sin t 1 } 3 2 } t 1 } 3 4 } sin 2 t 2 1 sin t 2 } 1 3 } sin 3 t 2 4 5 5 p 2 a 3 33. (a) Q w P w has length t , so P can be obtained by starting at Q and moving t sin t
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