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07_M_GOLD_9004_12_ch06-1

# 07_M_GOLD_9004_12_ch06-1 - Chapter 6 The Definite Integral...

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174 Chapter 6 The Definite Integral 6.1 Antidifferentiation 1. ( ) 2 1 ( ) 2 f x x F x x C = = + 2. ( ) 2 9 9 ( ) f x x F x x C = = + 3. ( ) 3 3 1 ( ) 3 x x f x e F x e C = = + 4. ( ) 3 3 1 ( ) 3 x x f x e F x e C = = − + 5. f ( x ) = 3 F ( x ) = 3 x + C 6. ( ) 2 4 ( ) 2 f x x F x x C = − = − + 7. 3 4 4 x dx x C = + 8. 2 1 1 3 3 6 x dx xdx x C = = + 9. 7 7 dx x C = + 10. 2 2 k dx k x C = + 11. 2 1 1 2 x dx xdx x C c c c = = + 12. 2 3 4 1 4 x x dx x dx x C = = + 13. 2 2 1 1 2 2 2 1 1 2 2 1 2ln 4 x dx x dx x x dx xdx x x x C + = + = + = + + 14. 1 1 1 1 ln 7 7 7 dx dx x C x x = = + 15. 3 2 5 2 2 5 x xdx x dx x C = = + 16. ( ) 1 2 1 2 1 2 1 2 1 2 3 2 3 2 2 2 2 2 2 2 4 4 3 4 4 3 x dx x x dx x x dx x dx x x C x x C + = + = + = + + = + + 17. 2 2 2 2 3 1 1 1 2 2 3 3 1 1 2 3 1 2 1 ln 2 3 3 x x dx x x dx x x xdx x dx dx x x x x C + = + = + = + + 18. 3 1 3 3 3 3 1 3 2 4 3 2 4 3 7 7 2 2 7 2 7 1 1 1 2 2 1 3 7 3 4 4 x dx x x dx x x dx x dx x x C x x C = = = + + = − + 19. 2 2 3 3 2 x x e dx e C = − + 20. x x e dx e C = − + 21. edx ex C = + 22. 2 2 2 7 7 7 2 4 2 x x x dx e dx e C e = = − + 23. ( ) 2 2 2 2 2 1 2 2 1 1 2 2 2 2 x x x x e dx e dx dx e x C e x C + = − = − + = − + 24. .5 .5 2 .5 2 .5 3 2 2 1 3 2 2 1 1 3 2 .5 3 x x x x x x x x e e x dx e dx xdx e dx e x e C e x e C + = − + = + + = + + 25. 2 2 2 5 2 5 2 t t t d ke ke e k dt = − = = − 26. /10 /10 /10 1 3 30 10 t t t d ke ke e k dt = = = 27. 4 1 4 1 4 1 1 4 2 2 x x x d ke ke e k dx = = =

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Section 6.1 Antidifferentiation 175 28. (3 1) (3 1) 3 1 (3 1) (3 1) 3 4 3 4 3 x x x x x d k d ke ke dx dx e ke e k + + + + + = = − = = − 29. 1 2 2 2 (5 7) (5 7) (5) 5 (5 7) (5 7) 1 5 d k x k x dx k x x k = − = − = = − 30. 3/ 2 1/ 2 1/ 2 3 ( 1) ( 1) ( 1) 2 2 3 d k x k x x dx k + = + = + = 31. 1 ln 4 ( 1) 4 4 4 1 d k k k x dx x x x k ⎤ = = = = − 32. 3 3 4 4 4 (8 ) (8 ) 3 (8 ) ( 1) 3 (8 ) 7(8 ) 7 3 d k d k x dx dx x k x k x x k = = − = = = 33. 5 4 4 4 (3 2) 5 (3 2) (3) 15 (3 2) (3 2) 1 15 d k x k x dx k x x k + = + = + = + = 34. 4 3 3 (2 1) 8 (2 1) (2 1) 1 8 d k x k x x dx k = = = 35. 3 [ ln 2 ] 3 2 2 d k k x k dx x x + = = = + + 36. ln 2 3 ( 3) 2 3 3 5 5 2 3 2 3 3 d k k x dx x k k x x ⎤ = = = = − 37.
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07_M_GOLD_9004_12_ch06-1 - Chapter 6 The Definite Integral...

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