O’zbekiston aloqa va axborotlashtirish agentligi toshkent axborot texnologiyalari universiteti samarqand filiali
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oliy matematikadan misol va masalalar toplami algebra va analitik geometriya limit uzluksizlik hosila integral. 1 qism.
68. . chx shx dx 69. x ch shx dx 2 . 70. . 3 x ch shx dx , cos , sin dx x R (bunda R rasional funksiya) ko’rinishdagi integrallarni hisoblang. 71. . cos 5 3 x dx 72. . cos 8 10 x dx 73. . cos 4 5 x dx 74. . sin 5 13 x dx 75. . sin 5 3 x dx 76. . sin 3 5 x dx 77. . cos x b a dx 78. . sin x b a dx Mustaqil yechish uchun misollarning javoblari 5.1. . 2 sin 4 1 2 1 C x x 5.2. . sin 3 1 sin 1 3 C px p px p 5.3. . cos 1 cos 3 1 3 C px p px p 5.4. . 4 sin 4 1 8 3 C px p x 5.5. . cos 5 1 cos 3 2 cos 5 3 C x x x 5.6. . cos ln 2 1 ) 6 2 C x x tg 5.7. . sin ln 2 1 2 C x ctg 5.8. . sin 5 1 sin 3 2 sin 5 3 C x x x 9. . 4 sin 32 1 2 sin 1 8 3 C px p px np x 10. . 4 sin 28 1 4 sin 8 1 C x x 11. . 8 sin 16 1 2 sin 4 1 C x x 12. . 5 sin 10 1 3 sin 6 1 C x x 13. . 10 cos 20 1 4 cos 8 1 C x x 14. . 2 cos 4 1 8 cos 16 1 C x x 15. . , 2 sin 2 sin 2 2 q p C q p x q p q p x q p 16. . , 2 sin 2 sin 2 2 q p C p q x p q q p x q p 17. . , 2 cos 2 cos 2 2 q p C q p x q p q p x q p 18. . 8 2 cos 16 4 cos 24 6 cos C x x x 19. . 4 sin 12 3 sin 28 7 sin 36 9 sin C x x x x 20. . 2 ln C x tg 21. . 2 ln 2 1 sin 2 cos 2 C x tg x x 104 22. . 3 1 2 3 sin 3 cos 3 3 C ctgx x ctg C ctgx x x 23. . 2 ln 8 3 sin cos 8 3 sin 4 cos 2 4 C x tg x x x x 24. . 3 2 5 1 3 5 C ctgx x ctg x ctg 25. . 2 4 ln C x tg 26. . 3 2 5 1 5 4 5 4 cos 5 sin 3 5 3 5 C tgx x tg x tg tgx x tg x x 27. . 2 ln 2 1 2 2 C x tg x sh chx 28. . 3 1 3 C cthx x cth 29. . 2 1 2 2 C shx arctg x ch shx 30. . 3 1 3 C thx x th 31. . ln 2 1 2 C chx x ch 32. . 2 2 ln sin C x tg x 33. . cos ln cos 2 1 2 C x x 34. . 2 4 ln sin sin 3 1 3 C x tg x x 35. . cos 1 C x 36. . C x tgx 37. . cos 1 cos C x x 38. . C shx arctg shx 39. . ln 2 1 2 C chx x ch 40. . 3 1 3 C shx arctg shx x sh 41. . C thx x 42. . 2 4 1 2 3 C thx x sh x 43. . 2 1 2 2 C shx arctg x ch shx 44. . 3 1 1 3 C x ch chx 45. . 3 1 3 C x thx x th 46. . 3 1 3 C x th 47. . 2 ln C x th chx 48. . ln 2 1 2 C shx x ch 49. . 2 ln 3 1 3 C x th chx x ch 50. . 4 sin 32 1 8 1 C x x 51. . sin 5 1 sin 3 1 5 3 C x x 52. . 6 sin 192 1 4 sin 64 1 2 sin 64 1 16 C x x x x 53. . sin 4 1 4 C x 54. . cos 3 1 cos 5 1 3 5 C x x 55. . 2 cos 3 5 cos 3 1 64 1 C x x 56. . 2 2 C x sh 57. . 4 32 1 8 C x sh x 58. . 15 2 5 1 3 2 3 C x sh x ch x sh 59. . 6 192 1 4 64 1 2 64 1 16 1 C x sh x sh x sh x 60. . 15 2 5 1 3 3 2 C x ch x ch x sh 5.105. 105 . 4 1 6 1 4 1 6 1 4 6 2 6 C x ch x ch x sh x sh 61. . ln C tgx 62. . 2 ln cos 1 C x tg x 63. . ln cos 2 1 2 C tgx x 64. . 2 ln cos 3 1 cos 1 3 C x tg x x 65. . sin 1 2 4 ln C x x tg 66. . 2 2 C x ctg 67. . ln sin 2 1 2 C tgx x 68. . ln C thx 69. . 2 ln 1 C x tg chx 70. . ln 2 1 2 C thx x th 71. . 2 2 2 2 ln 4 1 C x tg x tg 72. . 3 2 3 1 C x tg arctg 73. . 3 2 3 2 C x tg arctg 74. . 12 5 2 13 6 1 C x tg arctg 75. . 9 2 3 1 2 3 ln 4 1 C x tg x tg 76. . 4 3 2 5 2 1 C x tg arctg 77. . , 2 2 ln 1 , , 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 b a C b a x tg a b b a x tg a b a b b a C b a x tg b a arctg b a 78. . , 2 2 ln 1 , , 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 b a C a b b x atg a b b x atg a b b a C b a b x atg arctg b a 106 21-amaliy mashg’ulot. BA’ZI IRRASIONAL IFODALARNI INTEGRALLASH Quyidagi integrallarni hisoblang. 1. . 4 x x dx 2. . 3 x x dx 3. . 1 1 x dx 4. . 1 2 1 1 dx x x 5. . 2 4 3 x x x dx 6. . 1 1 1 1 3 dx x x . 7. dx x x 1 1 1 1 . 8. dx x x x x 1 1 1 1 . Quyidagi integrallarni (Eyler almashtirishlaridan foydalanib) hisoblang. 9. . 2 2 1 2 x x dx 10. . 3 4 4 2 x x x dx 11. . 1 1 2 x x x dx 12. . 1 2 x x x dx 13. . 5 2 x x x dx 14. . 4 2 x x x dx 15. . 2 2 x x x dx 16. . 8 6 3 2 x x dx x Quyidagi integrallarni, binomial differensiallarni integrallash usulidan foydalanib,hisoblang. 17. . 1 2 3 dx x x 18. . 1 1 2 3 6 dx x x 19. . 1 5 8 4 3 x x dx 20. . 1 2 3 x x dx 21. . 1 3 2 3 dx x x 22. . 1 2 3 3 dx x x 23. . 1 3 4 3 dx x x 24. 3 1 x x dx . Quyidagi integrallarni, , , 2 2 dx a x x R dx x a x R 2 2 , ifodalarni 107 integrallash usulidan foydalanib, hisoblang. 25. . 9 2 dx x 26. . 16 9 2 dx x 27. . 2 2 2 dx x b a 28. . 4 3 2 x dx 29. . 3 2 2 2 x b a dx 30. . 2 2 2 x b a x dx 31. . 2 2 2 dx x b a x m 32. . 2 2 2 2 dx x b a x Quyidagi integrallarni hisoblang. 33. . 9 3 2 x dx 34. . 25 2 2 x dx x Download 1.03 Mb. Do'stlaringiz bilan baham: |
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