AnswerKey12 - Answer Guide 12 Math 408C: Unique Numbers...

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Unformatted text preview: Answer Guide 12 Math 408C: Unique Numbers 56975, 56980, and 56985 Tuesday, December 1, 2009 Section 8.2 62. V = Z & & & sin 2 x ¡ 2 d x = 2 & Z &= 2 ¢ 1 & cos(2 x ) 2 £ 2 d x = & 2 Z &= 2 ¤ 1 & 2 cos(2 x ) + cos 2 (2 x ) ¥ d x = & 2 Z &= 2 ¢ 1 & 2 cos(2 x ) + 1 & cos(4 x ) 2 £ d x = & 2 ¢ 3 2 x & sin(2 x ) + 1 8 sin(4 x ) £ &= 2 = 3 8 & 2 : Section 8.3 4. Let x = 4 sin ¡ , where & &= 2 ¡ ¡ ¡ &= 2 . Then d x = 4 cos ¡ d ¡ , and p 16 & x 2 = 4 j cos ¡ j = 4 cos ¡ . When x = 0 , ¡ = arcsin(0) = 0 . When x = 2 p 3 , ¡ = arcsin ¦ p 3 2 § = &= 3 . So, Z x =2 p 3 x =0 x 3 p 16 & x 2 d x = Z ¡ = &= 3 ¡ =0 (4 sin ¡ ) 3 4 cos ¡ ¢ 4 cos ¡ d ¡ = 64 Z &= 3 sin 3 ¡ d ¡ = 64 Z ¡ = &= 2 ¡ =0 & 1 & cos 2 ¡ ¡ sin ¡ d ¡ = 64 Z u =1 = 2 u =1 (1 & u 2 ) d u = 40 3 : 1 6. Let x = sec & . Then d x = sec & tan & d & . When x = 1 , & = 0 . When x = 2 , & = arccos(1 = 2) = ¡= 3 . So, Z x =2 x =1 p x 2 & 1 x d x = Z & = ¡= 3 & =0 tan & sec & ¡ sec & tan & d & = Z ¡= 3 tan 2...
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This note was uploaded on 02/09/2010 for the course M 408c taught by Professor Mcadam during the Fall '06 term at University of Texas at Austin.

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AnswerKey12 - Answer Guide 12 Math 408C: Unique Numbers...

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