0 2 10 0 a 37 evaluate 1 0 11 0 12 0 sin1 x dx 13 e

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Unformatted text preview: 36. (a) 0 2 8. 0 1 √ 3 √ (b) 0 2 √ (c) 0 (d) 0 √ 9. 0 2 10. 0 a 37. Evaluate 1 0 11. 0 √ ∞ 12. 0 √ ∞ sin−1 x dx 13. e 1 ln x dx. x 14. e ∞ dx . x ln x dx . x(ln x)2 dx . x2 − 1 15. 0 x ln x dx. ∞ 16. e ∞ by using integration by parts even though the technique leads to an improper integral. 38. (a) For what values of r is ∞ 0 17. −∞ ∞ dx . 1 + x2 dx . x2 dx . x(x + 1) x x2 − 9 dx. 18. 2 3 xr e−x dx 19. −∞ ∞ 20. 22. dx . √ 3 3x − 1 1/ 3 0 convergent? (b) Use mathematical induction to show that ∞ 0 21. 1 5 x ex dx. −∞ 4 xn e−x dx = n!, n = 1, 2, 3, . . . . 23. 3 3 √ 24. 1 dx . 2−4 x x dx. (1 + x2 )2 1 dx. ex + e−x 39. The integral ∞ 0 √ 25. −3 1 dx . x(x + 1) x2 dx . −4 ∞ 1 dx x (1 + x) 26. 1 ∞ 27. −3 ∞ 28. −∞ 4 is improper...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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