RATSIONAL KASRLAR VA ULARNI INTEGRALLASHGA DOIR BA’ZI MASALALAR.
Keywords:
Ko‘phad * Ratsional kasr (funksiya) * Noto‘g‘ri ratsional kasr * To‘g‘ri ratsional kasr * I tur eng sodda ratsional kasr * II tur eng sodda ratsional kasrAbstract
Har qanday aniqmas integral elementar funksiyalar orqali ifodalanishi shart emas. Shu sababli elementar funksiyalarda ifodalanadigan integrallar sinfini topish masalasi paydo bo‘ladi. Bu masalaning xususiy bir javobi sifatida ratsional funksiyalardan olingan integrallarni ko‘rsatish mumkin. Bunda dastlab I-IV turdagi eng sodda ratsional funksiyalarni integrallash usuli ko‘rsatiladi. So‘ngra, ixtiyoriy ratsional funksiyani ularning algebraik yig‘indisi kabi yozish mumkinligidan foydalanib, umumiy holda ratsional funksiyadan olingan integrallarni hisoblash amalga oshiriladi. Bu integrallar logarifmik, arctg(ax+b) ko‘rinishdagi teskari trigonometrik funksiyalar hamda ratsional kasrlar, ya’ni elementar funksiyalar orqali ifodalanadi.
References
Latipova, S. (2024). YUQORI SINF GEOMETRIYA MAVZUSINI O’QITISHDA YANGI PEDAGOGIK TEXNOLOGIYALAR VA METODLAR. SINKVEYN METODI, VENN DIAGRAMMASI METODLARI HAQIDA. Theoretical aspects in the formation of pedagogical sciences, 3(3), 165-173.
Latipova, S. (2024, February). SAVOL-JAVOB METODI, BURCHAKLAR METODI, DEBAT (BAHS) METODLARI YORDAMIDA GEOMETRIYANI O’RGANISH. In Международная конференция академических наук (Vol. 3, No. 2, pp. 25-33).
Latipova, S., & Sharipova, M. (2024). KESIK PIRAMIDA MAVZUSIDA FOYDALANILADIGAN YANGI PEDAGOGIK TEXNOLOGIYALAR. 6X6X6 METODI, BBB (BILARDIM, BILMOQCHIMAN, BILIB OLDIM) METODLARI HAQIDA. Current approaches and new research in modern sciences, 3(2), 40-48.
Latipova, S. (2024). 10-11 SINFLARDA STEREOMETRIYA OQITISHNING ILMIY VA NAZARIY ASOSLARI. Академические исследования в современной науке, 3(6), 27-35.
Latipova, S. (2024). HILFER HOSILASI VA UNI HISOBLASH USULLARI. Центральноазиатский журнал образования и инноваций, 3(2), 122-130.
Latipova, S. (2024). HILFER MA’NOSIDA KASR TARTIBLI TENGLAMALAR UCHUN KOSHI MASALASI. Development and innovations in science, 3(2), 58-70.
Latipova, S. (2024). KESIK PIRAMIDA TUSHUNCHASI. KESIK PIRAMIDANING YON SIRTINI TOPISH FORMULALARI. Models and methods in modern science, 3(2), 58-71.
Shahnoza, L. (2023, March). KASR TARTIBLI TENGLAMALARDA MANBA VA BOSHLANG’ICH FUNKSIYANI ANIQLASH BO’YICHA TESKARI MASALALAR. In " Conference on Universal Science Research 2023" (Vol. 1, No. 3, pp. 8-10).
qizi Latipova, S. S. (2024). CAPUTO MA’NOSIDAGI KASR TARTIBLI TENGLAMALARDA MANBA FUNKSIYANI ANIQLASH BO ‘YICHA TO ‘G ‘RI MASALALAR. GOLDEN BRAIN, 2(1), 375-382.
Latipova, S. S. (2023). SOLVING THE INVERSE PROBLEM OF FINDING THE SOURCE FUNCTION IN FRACTIONAL ORDER EQUATIONS. Modern Scientific Research International Scientific Journal, 1(10), 13-23.
Latipova, S. (2024). GEOMETRIYADA EKSTREMAL MASALALAR. В DEVELOPMENT OF PEDAGOGICAL TECHNOLOGIES IN MODERN SCIENCES (Т. 3, Выпуск 3, сс. 163–172).
Latipova, S. (2024). EKSTREMUMNING ZARURIY SHARTI. В SOLUTION OF SOCIAL PROBLEMS IN MANAGEMENT AND ECONOMY (Т. 3, Выпуск 2, сс. 79–90).
Latipova, S. (2024). FUNKSIYANING KESMADAGI ENG KATTA VA ENG KICHIK QIYMATI. В CURRENT APPROACHES AND NEW RESEARCH IN MODERN SCIENCES (Т. 3, Выпуск 2, сс. 120–129).
Latipova, S. (2024). EKSTREMUMLARNING YUQORI TARTIBLI HOSILA YORDAMIDA TEKSHIRILISHI. IKKINCHI TARTIBLI HOSILA YORDAMIDA EKSTREMUMGA TEKSHIRISH. В SCIENCE AND INNOVATION IN THE EDUCATION SYSTEM (Т. 3, Выпуск 3, сс. 122–133).
Latipova, S. (2024). BIR NECHA O'ZGARUVCHILI FUNKSIYANING EKSTREMUMLARI. В THEORETICAL ASPECTS IN THE FORMATION OF PEDAGOGICAL SCIENCES (Т. 3, Выпуск 4, сс. 14–24).
Latipova, S. (2024). SHARTLI EKSTREMUM. В МЕЖДУРОДНАЯ КОНФЕРЕНЦИЯ АКАДЕМИЧЕСКИХ НАУК (Т. 3, Выпуск 2, сс. 61–70).
Latipova, S. (2024). KASR TARTIBLI HOSILALARGA BO'LGAN ILK QARASHLAR. В CENTRAL ASIAN JOURNAL OF EDUCATION AND INNOVATION (Т. 3, Выпуск 2, сс. 46–51).
Latipova, S. (2024). TURLI EKSTREMAL MASALALAR. BAZI QADIMIY EKSTREMAL MASALALAR. В CENTRAL ASIAN JOURNAL OF EDUCATION AND INNOVATION (Т. 3, Выпуск 2, сс. 52–57).
Latipova, S. (2024). FUNKSIYA GRAFIGINI YASASHDA EKSTREMUMNING QO'LLANILISHI. В CENTRAL ASIAN JOURNAL OF EDUCATION AND INNOVATION (Т. 3, Выпуск 2, сс. 58–65).
Latipova, S. (2024). BIRINCHI TARTIBLI HOSILA YORDAMIDA FUNKSIYANING EKSTREMUMGA TEKSHIRISH, FUNKSIYANING EKSTREMUMLARI. В CENTRAL ASIAN JOURNAL OF EDUCATION AND INNOVATION (Т. 3, Выпуск 2, сс. 66–72).
Sharipova, M., & Latipova, S. (2024). TAKRORIY GRUPPALASHLAR. Development of pedagogical technologies in modern sciences, 3(3), 134-142.
Shahnoza Latipova. (2024). THE STRAIGHT LINE AND ITS DIFFERENT DEFINITIONS. Multidisciplinary Journal of Science and Technology, 4(3), 771–780.
Sharipova, M., & Latipova, S. (2024). IKKI O’ZGARUVCHILI TENGLAMALAR SISTEMASI. Центральноазиатский журнал образования и инноваций, 3(2 Part 2), 93-103.
Latipova, S. (2024). THE STRAIGHT LINE AND ITS DIFFERENT DEFINITIONS. Multidisciplinary Journal of Science and Technology, 4(3), 771-780.
Latipova, S. (2024). KO ‘PO ‘ZGARUVCHILI FUNKSIYALARNING TURLI TA’RIFLARI. PEDAGOG, 7(5), 618-626.
Latipova Shahnoza. (2024). FAZODA ANALITIK GEOMETRIYANING SODDA MASALALARI. МЕДИЦИНА, ПЕДАГОГИКА И ТЕХНОЛОГИЯ: ТЕОРИЯ И ПРАКТИКА, 2(9), 406–419.
Jalolov, T. S. (2024). РАЗВИТИЕ ТЕХНОЛОГИЙ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА В САМОДВИЖАЩИХСЯ РОБОТАХ. Methods of applying innovative and digital technologies in the educational system, 1(2), 1-7.
Jalolov, T. S. (2024). ЭФФЕКТИВНОЕ ИСПОЛЬЗОВАНИЕ ТЕХНОЛОГИЙ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА В ЭКОНОМИЧЕСКОМ МОДЕЛИРОВАНИИ. Methods of applying innovative and digital technologies in the educational system, 1(2), 27-32.
