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Pre-Calc Homework Solutions 438

Pre-Calc Homework Solutions 438 - 438 Chapter 10 Review/3...

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44. Area 5 E p /3 0 } 1 2 } sin 2 3 u d u 5 } 1 2 } 3 } 1 2 } u 2 } 1 1 2 } sin (6 u ) 4 5 } 1 p 2 } 45. [ 2 3, 3] by [ 2 2, 2] The curves cross where cos 2 u 5 0, such as u 5 } p 4 } . Using the curves’ symmetry, Length 5 4 E p /4 0 } 1 2 } [(1 1 cos 2 u ) 2 2 1] d u 5 2 E p /4 0 (cos 2 2 u 1 2 cos 2 u ) d u 5 2 3 } 1 8 } sin 4 u 1 } 1 2 } u 1 sin 2 u 4 5 } p 4 } 1 2 46. [ 2 4.5, 4.5] by [ 2 2, 4] Since the two curves are covered over different u -intervals, find the two areas separately. Then Area 5 E 2 p 0 } 1 2 } [2(1 1 sin u )] 2 d u 2 p r 2 5 2 E 2 p 0 (1 1 2 sin u 1 sin 2 u ) d u 2 p 5 2 3 u 2 2 cos u 1 } 1 2 } u 2 } 1 4 } sin 2 u 4 2 p 5 5 p 47. } d d x t } 5 t , } d d y t } 5 2, so Area 5 E ˇ 5 w 0 2 p (2 t ) ˇ t 2 w 1 w 2 w 2 w dt 5 3 } 4 3 p } ( t 2 1 4) 3/2 4 5 } 76 3 p } 48. } d d x t } 5 2 t 2 } 2 1 t 2 } , } d d y t } 5 4, so Area 5 E 1 1/ ˇ 2 w 2 p 1 t 2 1 } 2 1 t } 2 ! 1 2 § t § 2 § } 2 § 1 t 2 } § 2 2 § 1 § 4 § 2 § dt , which using NINT evaluates to < 10.110. 49. } d d u r } 5 } ˇ 2 s c i o w n s w 2 2 w u u w } , so Area 5 E p /4 0 2 p ˇ co w s w 2 w u w sin u !
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