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Pre-Calc Homework Solutions 359

# Pre-Calc Homework Solutions 359 - Chapter 8 Review 46 u du...

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46. u 5 x dv 5 e 3 x dx du 5 dx v 5 } 1 3 } e 3 x E x e 3 x dx 5 } 1 3 } x e 3 x 2 E } 1 3 } e 3 x dx 5 } 1 3 } x e 3 x 2 } 1 9 } e 3 x 1 C E 0 2‘ x e 3 x dx 5 lim b 2‘ E 0 b x e 3 x dx 5 lim b 2‘ 3 } 1 3 } x e 3 x 2 } 1 9 } e 3 x 4 5 lim b 2‘ 3 2 } 1 9 } 2 } 1 3 } b e 3 b 1 } 1 9 } e 3 b 4 5 2 } 1 9 } 47. } t 2 ( 4 t t 2 3 1 1)( t t 2 2 1 1 1) } 5 } A t } 1 } t B 2 } 1 } t 2 C 1 } 1 } D t 2 t 1 1 1 E } 4 t 3 1 t 2 1 5 At ( t 2 1)( t 2 1 1) 1 B ( t 2 1)( t 2 1 1) 1 Ct 2 ( t 2 1 1) 1 ( Dt 1 E ) t 2 ( t 2 1) 5 ( A 1 C 1 D ) t 4 1 ( 2 A 1 B 2 D 1 E ) t 3 1 ( A 2 B 1 C 2 E ) t 2 1 ( 2 A 1 B ) t 2 B Equating coefficients of like terms gives A 1 C 1 D 5 0, 2 A 1 B 2 D 1 E 5 4, A 2 B 1 C 2 E 5 0, 2 A 1 B 5 1 and 2 B 5 2 1. Solving the system simultaneously yields A 5 0, B 5 1, C 5 2, D 5 2 2, E 5 1. E } t 2 ( 4 t t 2 3 1 1)( t t 2 2 1 1 1) } dt 5 E } d t 2 t } 1 E } t 2 2 dt 1 } 1 E } 2 t 2 2 t 1 1 1 1 } dt 5 E } d t 2 t } 1 E } t 2 2 dt 1 } 2 E } t 2 2 t 1 dt 1 } 1 E } t 2 1 1 dt 1 } 5 2 } 1 t } 1 2 ln ) t 2 1 ) 2 ln ) t 2 1 1 ) 1 tan 2 1 t 1 C 5 2 } 1 t } 1 ln } ( t t 2 2 1 1 1 ) 2 } 1 tan 2 1 t 1 C E 2‘ } t 2 ( 4 t t 2 3 1 1)( t t 2 2 1 1 1) } dt 5 E
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