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.
9. . 2 bx a x dx 10. . 3 2 2 x x dx 11. . 2 5 4 3 2 x x dx 12. . 2 fx c bx a dx 99 Integrallarni hisoblang: 13. . fx c bx a x dx 14. . 5 3 2 x x x dx 15. . 2 4 3 3 2 x x x dx 16. . 7 4 5 2 2 x x x dx 17. . 13 6 4 8 4 2 dx x x x 18. . 5 3 2 2 dx x x x Integrallarni hisoblang: 19. . 4 5 4 9 3 2 3 5 2 3 4 6 dx x x x x x x x 20. . 4 4 3 2 2 2 5 dx x x x x 21. . 1 3 6 5 4 3 2 2 2 3 4 dx x x x x x x 22. . 2 1 5 3 dx x x x Integrallarni hisoblang: 23. . 1 1 3 2 dx x x x 24. . 3 2 3 2 x x dx 25. . 3 2 1 3 2 x x x dx 26. . 1 3 2 2 dx x x Integrallarni hisoblang: 27. . 1 1 4 3 dx x x x 28. . 3 4 5 4 2 2 x x x x dx 29. . 8 6 6 2 4 3 dx x x x 30. . 4 13 9 2 3 2 4 2 x x dx x 31. . 4 2 3 2 2 3 2 2 2 x x x dx x x 32. . 2 2 20 9 11 18 2 2 dx x x x x x Mustaqil yechish uchun misollarning javoblari 1. . 1 2 ln 2 1 C x 2. . 2 5 ln 5 1 C x 3. . 7 5 2 3 ln 3 2 C x 4. . ln 1 C b x a a 5. . 3 1 ln 4 1 C x x 6. . 4 3 2 ln 5 1 C x x 7. . 1 4 ln 4 1 4 1 4 1 C x x 8. . ] 4 3 ln 3 1 4 3 1 [ 3 1 C x x 9. . ] ln 1 1 [ 1 C b x a a bx a a 10. . 3 2 ln 25 1 3 5 1 C x x x 11. . 2 5 4 3 ln 49 1 5 2 14 1 C x x x 12. . ln 1 2 C fx c bx a bc af b fx c af bc 100 13. . ln ln ln 1 C fx c bc af c c bx a bc af a b x ac 14. . 11 3 2 11 5 3 5 3 ln 10 1 2 2 C x arctg x x x 15. . 2 2 3 2 41 11 2 4 3 3 ln 82 1 2 2 C x arctg x x x 16. . 3 2 2 31 3 7 4 5 2 ln 93 1 2 2 C x arctg x x x 17. . 61 3 4 61 3 4 ln 61 2 5 13 6 4 ln 2 1 2 C x x x x 18. . 59 1 6 59 3 13 5 3 ln 6 1 2 C x arctg x x 19. . 2 1 1 2 ln 2 2 2 C x x x x x x 20. . 2 ln 72 2 27 30 6 3 4 4 2 3 4 C x x x x x x 21. . 5 3 2 5 3 2 ln 5 2 13 1 3 ln 2 5 11 2 3 3 2 2 2 3 C x x x x x x x 22. . 2 4 7 2 3 11 2 3 2 1 4 3 2 C x x x x 23. . 1 ln 2 1 2 C x x x 24. . 3 2 ln 625 3 3 2 250 6 21 16 2 2 C x x x x x x 25. . 3 2 1 ln 8 1 3 2 4 68 50 9 17 16 2 2 C x x x x x x x 26. . 1 1 ln 16 1 1 8 2 2 3 C x x x x x 27. . 2 1 1 ln 4 1 1 ln 4 3 C x arctg x x 28. . 2 130 7 5 4 ln 65 1 1 ln 20 1 3 ln 52 1 2 C x arctg x x x x 29. . 2 2 3 2 2 3 2 4 ln 2 2 C x arctg x arctg x x 30. . 2 5 3 2 5 3 ln 10 1 2 2 C x x x x 31. . 11 1 3 11 1 2 ln 2 1 C x arctg x x 32. . 1 5 4 ln C x arctg x x 101 20-amaliy mashg’ulot. TARKIBIDA TRIGONOMETRIK FUNKSIYALAR QATNASHGAN IFODALARNI INTEGRALLASH Integrallarni hisoblang. 1. . cos 2 dx x 2. . cos 3 pxdx 3. . sin 3 dx px 4. . cos 4 pxdx 5. . sin 5 xdx 6. . 3 dx tg 7. . 3 xdx ct 8. . cos 5 xdx 9. . sin 4 dx px dx qx px dx qx px dx qx px cos cos , sin sin , cos sin ko’rinishdagi integrallarni hisoblang. 10. . 9 cos 5 cos dx x x 11. . 3 sin 5 sin dx x x 12. . cos 4 cos dx x x 13. . 3 cos 7 sin dx x x 14. . 5 cos 3 sin dx x x 15. . cos cos dx qx px 16. . sin sin dx qx px 17. . cos sin dx qx px 18. . 3 sin 2 sin sin dx x x x 19. . 5 cos cos cos dx x x x dx x dx m m cos , sin ko’rinishdagi integrallarni hisoblang. 20. . sin x dx 21. . sin 3 x dx 22. . sin 4 x dx 23. . sin 5 x dx 24. . sin 6 x dx 25 . cos x dx 26. . cos 6 x dx 27. . 3 x sh dx 28. . 4 x sh dx 29. . 3 x ch dx 30. . 4 x ch dx 31. . 3 dx chx x sh dx x x dx x x q p q p cos sin , sin cos ko’rinishdagi integrallarni hisoblang. 32. . cos sin 2 dx x x 33. . cos sin 3 dx x x 34. . cos sin 4 dx x x 102 35. . cos sin 2 dx x x 36. . cos sin 2 2 dx x x 37. . cos sin 2 3 dx x x dx x ch x sh dx x sh x ch q p q p , ko’rinishdagi integrallarni hisoblang. 38. . 2 dx chx x sh 39. . 3 dx chx x ch 40. . 4 dx chx x sh 41. . 2 2 dx x ch x sh 42. . 2 3 dx x ch x sh 43. . 3 2 dx x ch x sh 44. dx x ch x sh 4 3 45. . 4 4 dx x ch x sh 46. . 4 2 dx x ch x sh 47. . 2 dx shx x ch 48. . 3 dx shx x ch 49. . 4 dx shx x ch xdx x q p cos sin ko’rinishdagi integrallarni hisoblang. 50. . cos sin 2 2 dx x 51. . cos sin 3 2 dx x x 52. . cos sin 4 2 dx x x 53. . cos sin 3 dx x x 54. . cos sin 2 3 dx x x 55. . cos sin 3 dx x x xdx ch x sh q p ko’rinishdagi integrallarni hisoblang. 56. . dx chx shx 57. . 2 2 dx x ch x sh 58. . 4 2 dx x ch x sh 59. . 2 3 x ch x sh 60. . 3 3 dx x ch x sh 61. . 2 3 dx x ch x sh x x dx q p cos sin ko’rinishdagi integrallarni hisoblang. 62. . cos sin x x dx 63. . cos sin 2 x dx 64. . cos sin 3 x x dx 65. . cos sin 4 x dx 66. x x dx cos sin 2 . 67. . cos sin 2 2 x x dx x xch sh dx q p ko’rinishdagi integrallarni hisoblang. |
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