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Business Calc Homework w answers_Part_73

Business Calc Homework w answers_Part_73 - 361 Chapter 8...

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56. } x 3 ( x 8 1 2) } 5 } x 1 A 2 } 1 } B x } 1 } x C 2 } 1 } x D 3 } 8 5 Ax 3 1 Bx 2 ( x 1 2) 1 Cx ( x 1 2) 1 D ( x 1 2) 5 ( A 1 B ) x 3 1 (2 B 1 C ) x 2 1 (2 C 1 D ) x 1 2 D Equating coefficients of like terms gives A 1 B 5 0, 2 B 1 C 5 0, 2 C 1 D 5 0, and 2 D 5 8 Solving the system simultaneously yields A 5 2 1, B 5 1, C 5 2 2, D 5 4 E } x 3 ( 8 x d 1 x 2) } 5 E } x 2 1 dx 2 } 1 E } d x x } 1 E } 2 2 x 2 dx } 1 E } 4 x d 3 x } 5 2 ln ) x 1 2 ) 1 ln ) x ) 1 } 2 x } 2 } x 2 2 } 1 C 57. t 3 1 t 5 t ( t 2 1 1) } 3 t 2 t 1 3 1 4 t t 1 4 } 5 } A t } 1 } B t 2 t 1 1 C 1 } 3 t 2 1 4 t 1 4 5 A ( t 2 1 1) 1 ( Bt 1 C ) t 5 ( A 1 B ) t 2 1 Ct 1 A Equating coefficients of like terms gives A 1 B 5 3, C 5 4 and A 5 4. Solving the system simultaneously yields A 5 4, B 5 2 1, C 5 4 E } 3 t 2 t 1 3 1 4 t t 1 4 } dt 5 E } 4 t dt } 1 E } 2 t 2 t 1 1 1 4 } dt 5 E } 4 t dt } 2 E } t 2 t 1 dt 1 } 1 E } t 2 4 1 dt 1 } 5 4 ln ) t ) 2 } 1 2 } ln ( t 2 1 1) 1 4 tan 2 1 t 1 C 58. t 4 1 4 t 2 1 3 5 ( t 2 1 3)( t 2 1 1) } ( t 2 1 1) 1 ( t 2 1 3) } 5 } A t 2 t 1 1 1 B } 1 } C t 2 t 1 1 D 3 } 1 5 ( At 1 B )( t 2 1 3) 1 ( Ct 1 D )( t 2 1 1) 5 ( A 1 C ) t 3 1 ( B 1 D ) t 2 1 (3 A 1 C ) t 1 3 B 1 D Equating coefficients of like terms gives A 1 C 5 0, B 1 D 5 0, 3 A 1 C 5 0, and 3 B 1 D 5 1 Solving the system simultaneously yields A 5 0, B 5 } 1 2 } , C 5 0, D 5 2 } 1 2 } E } ( t 2 1 3 d )( t t 2 1 1) } 5 E } t 2 1 1 /2 1 } dt 2 E } t 2 1 1 /2 3 } dt 5 } 1 2 } tan 2 1 t 2 } 2 ˇ 1 3 w } tan 2 1 } ˇ t 3 w } 1 C Evaluate the integrals using Formula 16, with x 5 t , a 5 1 in the first integral and a 5 ˇ 3 w in the second. 59. } x x 3 3 1 2 1 x } 5 1 1 } x x 3 1 2 1 x } 5 1 1 } x ( x x 2 1 2 1 1) } 5 1 1 } x ( x 2 x 1 1 )( x 1 1 1) } 5 } A x } 1 } x 2 B 1 } 1 } x 1 C 1 } x 1 1 5 A ( x 2 1)( x 1 1) 1 Bx ( x 1 1) 1 Cx ( x 2 1) 5 ( A 1 B 1 C ) x 2 1 ( B 2 C ) x 2 A Equating coefficients of like terms gives A 1 B 1 C 5 0, B 2 C 5 1, and 2 A 5 1. Solving the system simultaneously yields A 5 2 1, B 5 1, C 5 0 E } x x 3 3 1 2 1 x } dx 5 E dx 2 E } d x x } 1 E } x d 2 x 1 } 5 x 2 ln ) x ) 1 ln ) x 2 1 ) 1 C 60. } x 2 x 1 3 1 4 x 4 1 x 2 3 } 5 x 1 } x 2 1 2 4 3 x x 1 3 } 5 x 1 } ( x 1 2 1) 3 ( x x 1 3) } } ( x 1 2 1) 3 ( x x 1 3) } 5 } x 1 A 1 } 1 } x 1 B 3 } 2 3 x 5 A ( x 1 3) 1 B ( x 1 1) 2 3 x 5 ( A 1 B ) x 1 3 A 1 B Equating coefficients of like terms gives A 1 B 5 2 3, 3 A 1 B 5 0 Solving the system simultaneously yields A 5 } 3 2 } , B 5 2 } 9 2 } . E } x 2 x 1 3 1 4 x 4 1 x 2 3 } dx 5 E x dx 1 E } x 3 1 /2 1 } dx 2 E } x 9 1 /2 3 } dx 5 } x 2 2 } 1 } 3 2 } ln ) x 1 1 ) 2 } 9 2 } ln ) x 1 3 ) 1 C x x 2 1 4 x 1 3 q x 3 w 1 w 4 w x 2 w 1 w 0 w x w x 3 1 4 x 2 1 3 x }}}}} 2 3 x x 1 1 }} x ( x 2 1)( x 1 1) 1 x 3 2 x q x 3 w 1 w 0 w x 2 w 1 w x w 1 w 1 w x 3 1 0 x 2 2 x + 0 }}}}}}} x 1 1 Chapter 8 Review 361
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61.
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