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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online