Integrallash jadvalidan foydalanib integrallarni hisoblang.
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9. 10. ![](data:image/png;base64,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)
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23. 24. ![](data:image/png;base64,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)
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MAVZU: INTEGRALNI HISOBLASH USULLARI
Differensial belgisi ostiga kiritish usuli
Bu usulda integral ostidagi ifodalarni ko’rinishini o’zgartirish hisobiga jadval integraliga keltiriladi.
Bu usul bilan aniq misollar yordamida chuqurroq tanishib chiqamiz.
Misol. integralni hisoblang.
Yechish.![](data:image/png;base64,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)
Differensial belgisi ostiga kiritish usuli bilan quyidagi integrallarni hisoblang.
1. 2. ![](data:image/png;base64,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)
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7. 8. ![](data:image/png;base64,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)
9. 10.
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13. 14. ![](data:image/png;base64,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)
15. 16.
17. 18. ![](data:image/png;base64,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)
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21. 22.
23. 24.
25. 26. ![](data:image/png;base64,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)
27. 28.
29. 30.
Bo’laklab integrallash usuli
Faraz qilaylik, u(x), v(x) differensiallanuvchi funksiyalar bo’lsin. U holda yoki bo’lishi ravshan. Oxirgi tenglikni ikkala qismini integrallab yoki (33.2)
bo’laklab integrallash formulasi deb yuritiluvchi formulaga ega bo’lamiz.
Bo’laklab integrallashning mohiyati shundan iboratki, berilgan integralni hisoblashda integral ostidagi ifodani udv ko’paytma shaklida tasvirlab va (33.2) formulani tadbiq qilinsa, berilgan integralni jadval integrali yoki osongina topiladigan integral bilan almashtiriladi. Integrallarni bo’laklab integrallash usuli bilan hisoblashda muhim o’rinni u va dv ifodalarni qanday tanlanishi egallaydi.
Qanday hollarda larni qanday tanlashni qaraylik.
I. ![](data:image/png;base64,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)
turdagi integrallarni bo’laklab integrallash uchun deb olib qolgan ifodalarni dv orqali belgilash ma‘qul, bunda n- darajali ko’phad, а o’zgarmas son.
II.![](data:image/png;base64,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)
turdagi integrallarni bo’laklab integrallash uchun transendent ko’paytuvchini u va deb olish maqsadga muvofiq.
III. (a,b-o’zgarmas sonlar) turdagi integrallar uchun esa va qolgan ko’paytuvchilarni dv deb olish ma‘qul.
Bo’laklab integrallash jarayoniga tegishli belgilashlarni ham xuddi o’zgaruvchini almashtirish usulidagidek integraldan so’ng vertikal kesmalar orasiga yozamiz.
Misol. integral hisoblansin.
Yechish. desak bo’lib, (33.2) formulaga binoan kelib chiqadi.
Bo’laklab integrallash usulidan foydalanib integrallarni hisoblang.
1. 2. ![](data:image/png;base64,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)
3. 4.
5. 6. ![](data:image/png;base64,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)
7. 8.
9. 10. ![](data:image/png;base64,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)
11. 12.
13. 14. ![](data:image/png;base64,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)
15. 16.
17. 18. ![](data:image/png;base64,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)
19. 20.
21. 22. ![](data:image/png;base64,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)
23. 24.
25. 26. ![](data:image/png;base64,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)
27. 28.
29. 30. ![](data:image/png;base64,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)
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