Fall 2002 Improper Integrals From Old Exams - Mat104 Fall 2002 Improper Integrals From Old Exams For the following integrals state whether they are

Thomas' Calculus: Early Transcendentals

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Mat104 Fall 2002, Improper Integrals From Old Exams For the following integrals, state whether they are convergent or divergent, and give your reasons. 1. 0 dx x 3 + 2 2. 1 0 dx x + x 3. 1 1 + x x 3 4. 0 x 2 x 3 + 1 dx 5. 1 0 ln x dx 6. 1 0 dx e x - 1 7. 0 dx x 2 + 2 x + 2 8. 1 x 3 ln x + x 4 dx 9. 0 dx x 3 + x 10. 1 0 dx 1 - cos x 11. 0 e - x cos x dx 12. 0 e - x 2 x 2 dx 13. 0 x 2 + 10 3 x 5 + 6 x + 8 dx 14. 0 x 4 + 3 x + 1 x 5 + 2 x 2 + 3 dx 15. 1 0 e x x dx 16. 1 0 sin x x dx 17. 1 0 dx x 2 + x 18. 1 0 (1 - x ) - 2 / 3 dx 19. 2 x 2 + 4 x + 4 ( x - 1) 3 · x 3 - 1 dx 20. π/ 2 0 tan x dx 21. 0 e x - 1 e 2 x + 1 dx 22. 2 sin x x 2 - 1 dx 23. 1 sin x x + x 4 dx 24. 1 0 sin x x + x 4 dx 25. 2 0 dx | x - 1 | 26. 1 dx x 0 . 99 27. 0 dx x 4 + x 2 / 3 dx 28. 0 x 3 e - x dx 29. 1 ln x 1 + x 2 dx 30. 1 dx x 2 ln x 31. π/ 2 0 dx sin x 32. 0 e x (1 + e - 2 x ) dx 33. 1 0 x ln x dx 34. 2 dx x 3 - 1 35. π/ 2 0 1 + cos x x dx 36. 1 ln x ·

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