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.
35. . 2 2 2 2 x b a dx x 36. . 4 2 3 dx x x 37. . 2 2 2 3 dx x b a x 38. . 2 2 2 4 dx x b a x 39. . 2 2 2 2 x b a x dx 40. . 2 2 2 4 x b a x dx Mustaqil yechish uchun misollarning javoblari 1. . 1 ln 4 4 2 4 4 C x x x 2. . ] 1 ln 2 1 . 3 1 [ 6 6 6 3 C x x x x 3. . 1 1 ln 2 1 2 C x x 4. . 2 1 ln 2 1 2 1 C x x x 5. 12 6 4 3 48 6 8 3 2 x x x x x 2 ln 2 33 1 ln 3 12 6 12 x x x C x arctg 7 1 2 7 171 12 .6. . 1 , 6 1 ln 3 7 6 5 6 2 3 3 6 6 2 7 5 4 2 x t C arctgt t t t t t t 7. . 1 1 ln 4 1 4 C x x x 8. . 1 ln 2 1 1 2 1 2 1 2 2 2 C x x x x x 9. . 2 2 2 2 2 2 1 ln 2 2 C x x x x x x 10. . 3 3 4 4 2 3 3 4 4 2 ln 3 1 2 2 C x x x x x x 11. . 1 1 2 2 C x x x x arctg 12. , 1 ln 2 3 1 3 1 ln 2 1 ln 2 C t t t t bunda 108 . 1 1 2 x x x t 13. . 5 5 5 5 ln 5 1 2 2 C x x x x x x 14. , 1 5 1 ln 2 15 1 ln 2 1 1 2 ln 8 C t t t t bunda . 2 4 2 x x x t 15. . 2 2 1 2 2 ln 2 1 2 C x x x 16. . 2 8 6 8 6 2 2 2 2 C x x x x x x 17. . 3 11 24 7 3 3 / 4 6 / 11 3 / 7 C x x x 18. . 1 3 1 1 ln 2 9 6 3 6 6 6 6 C x x x x x 19. . 1 2 1 3 8 4 8 3 8 C x x 20. . 1 1 1 ln 3 3 3 3 C x x x 21. . 1 2 2 / 3 3 C x 22. x x x arctg x x x x 3 1 2 3 1 1 1 1 ln 6 1 3 3 3 3 2 3 2 3 . 1 1 1 ln 3 1 3 3 3 3 C x x x x 23. . 1 1 7 4 3 / 4 4 3 3 / 7 4 3 C x x 24. . 1 1 1 1 ln 3 1 3 3 C x x 25. . 3 sin 2 9 2 9 2 C x arc x x 26. . 4 3 sin 8 9 2 16 9 2 C x arc x x 27. . sin 2 2 2 2 2 2 C a bx arc a x b a x b 28. . 4 4 2 C x x 29. . 2 2 2 2 C x b a a x 30. . ln 1 2 2 2 C bx x b a a a 31. . 2 2 2 2 2 2 C b m x b a m 32. . arcsin 8 8 2 3 4 2 2 2 2 2 3 2 C a bx b a x b a b x a x b 33. . 9 9 2 C x x 34. . 5 sin 2 25 2 25 2 C x arc x x 35. . sin 2 2 3 2 2 2 2 2 C a bx arc b a b x b a 36. . 4 3 8 2 2 C x x 37. . 3 2 2 2 2 4 2 2 2 C x b a b x b a 38. . sin 8 3 8 3 2 5 4 2 2 2 4 2 3 2 C a bx arc b a x b a b x a x b 39. . 2 2 2 2 C x a x b a 40. . 3 2 2 2 2 3 4 2 2 2 C x b a x a x b a 109 22-amaliy mashg’ulot. ANIQ INTEGRALNI HISOBLASH. NYUTON-LEYBNIS FORMULASI Quyidagi integrallarni, Nyuton – Leybnis formulasiga asosan, hisoblang. 1. 1 0 3 2 dx x . 2. . 5 0 1 4 dx x 3. dx x 4 1 2 . 4. . 1 2 5 1 dx x 5. . 2 1 0 2 dx x x 6. 2 1 2 . 4 3 dt t t 7. . cos 1 0 dx 8. . 1 0 2 dx x x 9. dx x x 1 0 2 1 2 3 Quyidagi integrallarni, Nyuton – Leybnis formulasiga asosan, hisoblang. 10. . 7 4 3 1 1 2 dx x x 11. . 4 2 1 2 dx x 15. . 4 1 t t dt 16. . 1 2 36 1 0 3 dx x 17. . 1 2 / 3 3 / 2 1 8 / 1 3 / 1 dx x x 18. 0 2 . 5 sin xdx 19. 3 / 0 2 . sec tdt 20. . 2 3 2 dx x ctg 21. . sec 0 3 xtgxdx . Quyidagi integrallarga, Nyuton–Leybnis formulasini formal ravishda qo’llaganda, noto’g’ri natijaga kelinishini izohlang. 22. . cos 2 0 2 2 dx x x tg dx 23. . 1 1 1 dx x arctg dx d 24. . 1 1 x dx Quyidagi integrallarni hisoblang. 25. . 5 2 0 2 dx x 26. . 1 0 2 dx x x 27. . 1 1 3 dx x 28. . 2 1 3 dx x 28. . 1 3 3 / 1 2 x dx 29. . 1 9 2 3 dx x 30. . cos 1 0 dx x 31. . cos 4 3 4 dх х ec 32. . sin 8 2 2 2 dy y y 110 33. . 4 1 2 2 1 5 2 du u 34. . 4 4 dx x 35. . 6 6 dx x х Quyidagi integrallarni hisoblang. 36. . 3 2 0 dx x 37. . 1 1 0 6 2 x dx x 38. . ln 3 2 e e x x dx 39. . sin 2 dx x 40. 1 0 2 . 5 4 4 x x dx 41. . 8 2 3 2 2 x x dx 42. . ln cos 1 e x dx x 43. . ln 1 1 2 e x x dx 44. . 4 1 0 2 dx x Quyidagi aniq integrallarni, o’zgartiruvchilarni almashtirish yordamida, hisoblang. 45. . 1 3 0 dy y 46. . 1 0 1 dx y 47. 0 2 . sin cos 3 dx x 48. 3 2 2 . sin cos xdx x 49. . 4 5 1 1 2 2 dx x x 50. . 4 5 1 0 2 2 dx x x 51. 6 0 . 3 sin 3 cos 1 tdt t 52. 3 / 6 3 sin 3 cos 1 tdt t . 53. . sin 3 4 cos 2 0 dt t t 54. . sin 3 4 cos dt t t 55. . 2 5 2 1 0 4 5 dx x x x 56. . 2 sin 2 cos 6 0 3 хdх х Quyidagi integrallarni, o’zgaruvchilarni almashtirish usulidan foydalanib, hisoblang. 57. . 1 2 1 2 x x dx 58. . 1 0 x x x e e dx e 59. . 9 6 3 4 2 dx x x 60. . 0 2 2 a x a x dx 61. . cos sin 1 2 0 x x dx 62. . 1 sin 1 0 dx x x x arc 63. Ushbu dx x x 7 1 2 13 6 integralda, t x x 13 6 2 almashtirishni olish mumkinmi? Javobingizni sharhlang. 111 64.Ushbu 1 0 2 1 dx x integralda, t x sin almashtirishni olish mumkinmi? Javobingizni sharhlang. 65.Ushbu 0 2 sin 1 x dx integralda, t tgx almashtirishni olish mumkinmi? Javobingizni sharhlang. Bo’laklab integrallash formulasi yordamida, aniq integrallarni hisoblang. 66. . 4 0 dx xe x 67. 2 1 . ln xdx x 68. . 2 sin 2 / 0 2 tdt t 69. 1 0 2 . dx x arctg x 70. . 3 / 0 2 xdx tg x 71. . ln 2 1 3 xdx x 72. . 1 0 2 dx e x x 73. . ln 2 1 e dx x x 74. . ln 2 1 e dx х 75. . cos 2 / 1 0 xdx x Download 1.03 Mb. Do'stlaringiz bilan baham: |
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