IKKI KARRALI INTEGRALLAR
DOI:
https://doi.org/10.37547/Keywords:
Ikki karrali integral, takroriy integral, yuz elementi, integrallanuvchanlik sharti, additivlik, o‘rta qiymat teoremasi, qutb koordinatalari, yakobian, koordinata almashtirishi, integrallash tartibini almashtirish, geometrik tatbiqlar, hajm hisoblash, fizik tatbiqlar, tekis plastinka massasi, statik moment, massa markazi, inersiya momenti.Abstract
Ushbu maqolada ikki karrali integralning asosiy tushunchalari, uning geometrik (jism hajmi va soha yuzasi) va fizik (massa, statik momentlar, massa markazi, inersiya momentlari) ma’nolari batafsil yoritilgan. Integralning mavjudlik sharti, chiziqlilik, additivlik, monotonlik va o‘rta qiymat teoremasi kabi asosiy xossalari keltirilgan. Ikki karrali integralni to‘g‘ri to‘rtburchak va ixtiyoriy shakldagi sohalarda takroriy integralga keltirib hisoblash usullari ko‘rsatilgan, integrallash tartibini almashtirish texnikasi misol bilan tahlil qilingan. Qutb koordinatalariga o‘tish va yakobian yordamida koordinata almashtirishning ahamiyati, ayniqsa aylana va halqa shaklidagi sohalar uchun, misollar bilan izohlangan. Maqolaning amaliy qismida to‘liq hisoblash misollari (yuz, hajm, massa, massa markazi) keltirilib, ularning bosqichma-bosqich yechimi berilgan. Maqola oliy matematikaning «Ko‘p o‘zgaruvchili funksiyalar integral hisobi» bo‘limini chuqurroq o‘zlashtirmoqchi bo‘lgan talabalar, magistrantlar va mustaqil izlanuvchilar uchun mo‘ljallangan. Nazariy ma’lumotlar soddalashtirilgan va tizimli ravishda, misollar bilan mustahkamlangan holda bayon qilingan.
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