Pre-Calc Homework Solutions 243

Pre-Calc Homework Solutions 243 - Section 6.2 8 u du du 1...

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8. u 5 y 4 1 4 y 2 1 1 du 5 (4 y 3 1 8 y ) dy du 5 4( y 3 1 2 y ) dy } 1 4 } du 5 ( y 3 1 2 y ) dy E 8( y 4 1 4 y 2 1 1) 2 ( y 3 1 2 y ) dy 5 8 1 } 1 4 } 2 E u 2 du 5 } 2 3 } u 3 1 C 5 } 2 3 } ( y 4 1 4 y 2 1 1) 3 1 C Check: } d d x } 3 } 2 3 } ( y 4 1 4 y 2 1 1) 3 1 C 4 5 2( y 4 1 4 y 2 1 1) 2 (4 y 3 1 8 y ) 5 8( y 4 1 4 y 2 1 1) 2 ( y 3 1 2 y ) 9. Let u 5 1 2 x du 5 2 dx E } (1 2 dx x ) 2 } 5 2 E } d u u 2 } 5 u 2 1 1 C 5 } 1 2 1 x } 1 C 10. Let u 5 x 1 2 du 5 dx E sec 2 ( x 1 2) dx 5 E sec 2 u du 5 tan u 1 C 5 tan ( x 1 2) 1 C 11. Let u 5 tan x du 5 sec 2 x dx E ˇ ta w n w x w sec 2 x dx 5 E u 1/2 du 5 } 2 3 } u 3/2 1 C 5 } 2 3 } (tan x ) 3/2 1 C 12. Let u 5 u 1 } p 2 } du 5 d u E sec 1 u 1 } p 2 } 2 tan 1 u 1 } p 2 } 2 d u 5 E sec u tan u du 5 sec u 1 C 5 sec 1 u 1 } p 2 } 2 1 C 13. Let u 5 ln x du 5 } 1 x } dx E 6 e } x d ln x x } 5 E ln 6 1 } d u u } 5 ln ) u ) 4 5 ln (ln 6) 14. Let u 5 tan x du 5 sec 2 x dx E p /4 2 p /4 tan 2 x sec 2 x dx 5 E 1 2 1 u 2 du 5 } 1 3 } u 3 4 5 } 1 3 } (1) 2 } 1 3 } ( 2 1) 3 5 } 1 3 } 1 } 1 3 } 5 } 2 3 } 15. Let u 5 3 z 1 4 du 5 3 dz } 1 3 } du 5 dz E cos (3 z 1 4) dz 5 } 1 3 } E cos u du 5 } 1 3 } sin u 1 C 5 } 1 3 } sin (3 z 1 4) 1 C 16. Let u 5 cot x du 5 2 csc 2 x dx E ˇ co w t w x w csc 2 x dx 5 2 E u 1/2 du 5 2 } 2 3 } u 3/2 1 C 5 2 } 2 3 } (cot x ) 3/2 1 C 17.
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