Business Calc Homework w answers_Part_57

Business Calc Homework w answers_Part_57 - Chapter 6 Review...

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10. Let u 5 3 x 1 4 du 5 3 dx } 1 3 } du 5 dx E 5 } 1 3 } E u 2 1/3 du 5 } 1 3 } ? } 3 2 } u 2/3 1 C 5 } 1 2 } (3 x 1 4) 2/3 1 C 11. Let u 5 t 2 1 5 du 5 2 t dt } 1 2 } du 5 t dt E } t 2 t 1 dt 5 } 5 } 1 2 } E } 1 u } du 5 } 1 2 } ln ) u ) 1 C 5 } 1 2 } ln ) t 2 1 5 ) 1 C 5 } 1 2 } ln ( t 2 1 5) 1 C 12. Let u 5 } 1 u } du 52} u 1 2 } d u E } u 1 2 } sec } 1 u } tan } 1 u } d u 52 E sec u tan u du sec u 1 C sec } 1 u } 1 C 13. Let u 5 ln y du 5 } 1 y } dy E } tan ( y ln y ) } dy 5 E tan u du 5 E } c s o in s u u } du Let w 5 cos u dw sin u du E } w 1 } dw 5 ln ) w ) 1 C ln ) cos u ) 1 C ln ) cos (ln y ) ) 1 C 14. Let u 5 e x du 5 e x dx E e x sec ( e x ) dx 5 E sec u du 5 ln ) sec u 1 tan u ) 1 C 5 ln ) sec ( e x ) 1 tan ( e x ) ) 1 C 15. Let u 5 ln x du 5 } 1 x } dx E } x d ln x x }5 E } 1 u } du 5 ln ) u ) 1 C 5 ln ) ln x ) 1 C 16. E } t ˇ dt t w } 5 E } t d 3/ t 2 } 5 E t 2 3/2 dt 2 t 2 1/2 1 C ˇ 2 t w } 1 C 17. Use tabular integration with f ( x ) 5 x 3 and g ( x ) 5 cos x . E x 3 cos x dx 5 x 3 sin x 1 3 x 2 cos x 2 6 x sin x 2 6 cos x 1 C 18. Let u 5 ln xd v 5 x 4 dx du 5 } 1 x } dx v 5 } 1 5 } x 5 E x 4 ln x dx 5 } 1 5 } x 5 ln x 2 E } 1 5 } x 5 1 } 1 x } 2 dx 5 } 1 5 } x 5 ln x 2 } 1 5 } E x 4 dx 5 } 1 5 } x 5 ln x 2 } 2 1 5 } x 5 1 C x 3 3 x 2 6 x 6 0 (+) (–) (+) (–) cos x sin x –cos x –sin x cos x f ( x ) and its derivatives g ( x ) and its integrals dx } ˇ 3 3 w x w 1 w 4 w Chapter 6 Review 281
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19. Let u 5 e 3 x dv 5 sin x dx du 5 3 e 3 x dx v 52 cos x E e 3 x sin x dx e 3 x cos x 1 E 3 cos x e 3 x dx Integrate by parts again. Let u 5 3 e 3 x dv 5 cos x dx du 5 9 e 3 x dx v 5 sin x E e 3 x sin x dx e 3 x cos x 1 3 e 3 x sin x 2 E 9 e 3 x sin x dx 10 E e 3 x sin x dx e 3 x cos x 1 3 e 3 x sin x 1 C E e 3 x sin x dx 5 } 1 1 0 } [ 2 e 3 x cos x 1 3 e 3 x sin x ] 1 C 5 1 } 3s 1 i 0 n x } 2 } co 1 s 0 x } 2 e 3 x 1 C 20. Let u 5 x 2 dv 5 e 2 3 x dx du 5 2 x dx v 52} 1 3 } e 2 3 x E x 2 e 2 3 x dx 1 3 } x 2 e 2 3 x 1 } 2
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Business Calc Homework w answers_Part_57 - Chapter 6 Review...

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