ikkinchi tur egri chiziqli integrallar

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mavzu: ikkinchi tur egri chiziqli integrallar reja: 1. ikkinchi tur egri chiziqli integralning ta’rifi. 2. ikkinchi tur egri chiziqli integralni aniq integral yordamida hisoblash. 3. birinchi va ikkinchi tur egri chiziqli integrallar orasidagi bog’liqlik. 4. ikkinchi tur egri chiziqli integralning fizikaga tadbiqi. 1. ikkinchi tur egri chiziqli integralning ta’rifi (i) parametric tenglamalar bilan berilgan chiziq to’g’rilanuvchi ochiq egri chiziq bo’lib, unda funktsiyalar berilgan bo’lsin. [] segmentni nuqtalar yordamida n ta bo’lakka ajratsak, l=ab chiziq a=m0 , m1 m2,….m4=b nuqtalar yordamida a dan b ga yo’nalgan n ta bo’lakka (yoychalarga) bo’linadi. faraz qilaylik bo’lsin, va har bir yoyda nuqta olib integral yig’indilarni tuzamiz. ta’rif: agar limit mavjud bo’lsa, u holda y 2-tur egri chiziqli integral deyiladi va deb belgilanadi. 5-chizma i1+i2 yig’indi umumiy ikkinchi tur egri chiziqli integral deyiladi va quyidagicha belgilanadi: (2) agar ab chiziqda integrallash yo’nalishi o’zgartirilsa, ta’rifga ko’ra ikkinchi tur egri chiziqli integralning ishorasi o’zgaradi: agar a nuqta …
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orasidagi bog’liqlik teorema. l=ab (i) tenglamalar bilan berilgan silliq egri chiziq, bo’lsin funktsiyalar ab chiziqda uzluksiz, birlik vektor ab chiziqga uning m(x,y) nuqtasida o’tkazilgan urunma vektor bo’lib, yo’nalishi a dan b ga qarab bo’lsin, burchak m(x,y) nuqtada vektor bilan ox o’qi orasidagi burchak bo’lsin. u holda (6) tenglik o’rinlidir, bunda izoh: fazoviy egri chiziq esa 8-chizma bo’ladi, bu yerda va bo’lib vektor bilan mos ravishda ox, oy va oz o’qlari orasidagi burchaklardir. 4. ikkinchi tur egri chiziqli integralning fizikaga tadbiqi 4.1 massasi birga teng moddiy nuqtaning a dan b ga qarab ko’chirishda, kuchning bajargan ishini a desak, u vaqtda ma’lumki bo’ladi. 4.2 vektor m(x,y) nuqtadan oqib o’tuvchi suyuqlik tezligi bo’lsin. u holda, birlik vaqt ichida g sohadan oqib o’tuvchi suyuqlik miqdori bo’ladi, bu yerda vektor m(x,y) nuqtada l chiziqga o’tkazilgan tashqi normal vektorning birlik vektoridir. agar bo’lib, urunma vektorning l da yo’nalishi musbat yo’nalish bilan mos tushsa, u holda bo’lib, …
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garuvchi x, +1 dan -1 gacha o’zgaradi va uning uchun 3-misol. tenglama bilan berilgan l- chiziq bo’yicha olingan integralni hisoblang. berilgan tenglama bilan aylana aniqlanadi, uning parametrik tenglamalari ko’rinishga ega. integralni (4) formula yordamida hisoblaylik. bo’lgani uchun 4-misol. tenglamalar bilan berilgan l-chiziq bo’yicha. integralni o’sish yo’nalishi bo’yicha hisoblang. berilgan integralni (4) formula yordamida hisoblaylik, bo’lgani uchun 5-misol sferani i oktantda joylashgan qismi chegarasi bo’lgan l yopiq chiziq bo’yicha olingan integralni hisoblang. oxy tekislikda yo’nalish a(i; 0; 0) nuqtadan b (0; i; 0) nuqtaga qarabdir. bo’lib, chiziqlar mos ravishda oxy, oyz va oxz tekisliklarda yotuvchi birlik aylana bo’laklaridir. shuning uchun i=i1+i2+i3 deb olsak, u vaqtda bo’ladi. 11-chizma i1 integralni hisoblashda ni oxy tekislikda yotishini hisobga olsak, z=0 va dz=0 bo’ladi hamda bo’ladi. chiziq bo’lib, uning parametrik tenglamalari esa ko’rinishga ega. demak (4) formulaga asosan bu yerda geometrik jihatdan ekanini hisobga oldik. i2 va i3 integrallar ham shunga o’xshash hisoblanadi va bo’ladi …
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mavzu: ikkinchi tur egri chiziqli integrallar reja: 1. ikkinchi tur egri chiziqli integralning ta’rifi. 2. ikkinchi tur egri chiziqli integralni aniq integral yordamida hisoblash. 3. birinchi va ikkinchi tur egri chiziqli integrallar orasidagi bog’liqlik. 4. ikkinchi tur egri chiziqli integralning fizikaga tadbiqi. 1. ikkinchi tur egri chiziqli integralning ta’rifi (i) parametric tenglamalar bilan berilgan chiziq to’g’rilanuvchi ochiq egri chiziq bo’lib, unda funktsiyalar berilgan bo’lsin. [] segmentni nuqtalar yordamida n ta bo’lakka ajratsak, l=ab chiziq a=m0 , m1 m2,….m4=b nuqtalar yordamida a dan b ga yo’nalgan n ta bo’lakka (yoychalarga) bo’linadi. faraz qilaylik bo’lsin, va har bir yoyda nuqta olib integral yig’indilarni tuzamiz. ta’rif: agar limit mavjud bo’lsa, u holda y 2-tur egri...

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