trigonometrik funksiyalarni integrallash

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types of lesson plan mavzu: trigonometrik funksiyalarni integrallash yevdoks knidskiy e.av. 408 — 355 yillar. integral hisob matematika rivojlanishining antik davrlariga borib taqaladi. qadimgi yunonistonda sirt va hajmlarni aniqlashning yevdoks knidskiy tomonidan ishlab chiqilgan ma’lum metodlari ba’zi sodda integrallarni hisoblash imkonini bergan leybnits gotfrid vilgelm (1646-1716) ∫ belgi leybnits tomonidan 1675 yilda kiritilgan. bu belgi lotin alifbosidagi s harfining o’zgartirilgan ko’rinishidir. (summa so’zidagi birinchi harf). gotfrid vilgelm leybnits (1646—1716) isaak nyuton (1643 – 1727) nyuton va leybnitslar bir - birlaridan bexabar ravishda integral uchun nyuton – leybnits formulasini ishlab chiqishdi. ostyugen luyi koshi (1789 – 1857) karl tedor vilgelm veyershtrass (1815 1897 ) koshi va veyshtrasning ishlari integral hisobning ko’p yillik rivojlanishining cho’qqisi bo’ldi. rus matematiklardan quyidagi olimlar integral hisoblash usullariga o’z hissalarini qo’shishdi: m.b.ostogradskiy (1801 – 1862) b.bunyakovskiy (1804 – 1889) p.l.chebishev (1821 – 1894) 1. ko`rinishdagi intеgralni topish integralni topishning universal usuli mavjud bo`lib, bu usul bilan integralni …

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`ni u holda almashtirish yordamida ratsional funksiyani intеgrallashga kеltiriladi. 2-misol. ko`rinishdagi intеgralni qaraymiz (m va n lar butun sonlar) misol: va ko`rinishdagi integrallarni topish. misol: integral topilsin. 4. ko’rinishdagi integrallarni topish misol. integralni toping foydalanilgan adabiyotlar 1. gerd baumann. mathematics for engineers i. basic calculus. oldenbourg verlag munchen 2010. 2. gerd baumann. mathematics for engineers ii. calculus and linear algebra oldenbourg verlag munchen 2010. 3. claudio canuto, anta tabacco. mathematical analysis i, ii. springer-verlag, italia, 2008 4. соатов ё.у олий математика. 1-5 қисмлар. -т.: ўқитувчи, 1995. 5. danko p.s., popov a.g., kojevnikova t.ya. oliy matematika misol va masalalarda, 1-qism. -t.: o'zbekiston faylasuflar milliy jamiyati, 2007. image2.jpeg image3.png image4.jpeg image5.png image6.jpeg image7.png image8.png image9.png image10.png image11.wmf image12.wmf image13.wmf image14.wmf oleobject1.bin oleobject2.bin oleobject3.bin oleobject4.bin image15.wmf oleobject5.bin image16.wmf image25.wmf image26.wmf image27.wmf image28.wmf image29.wmf image30.wmf image31.wmf image17.wmf image18.wmf image19.wmf image20.wmf image21.wmf image22.wmf image23.wmf image24.wmf oleobject10.bin oleobject11.bin oleobject12.bin oleobject13.bin oleobject14.bin oleobject15.bin oleobject16.bin oleobject17.bin oleobject18.bin oleobject19.bin …

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s , x (sin r ) x cos , x sin ( r - == - z x cos = ) x cos , x (sin r z ) x cos , x (sin r x cos ) x cos , x (sin r ) x cos , x (sin r - = - 2 sincos ixxdx = ò ò × xdx cos x sin n m xdx cos x sin 5 4 ò ò xdx tg m ò xdx ctg m 3 tgxdx ò sincos axbxdx × ò coscos axbxdx × ò sinsin axbxdx × ò ò × dx x sin x sin 3 5

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types of lesson plan mavzu: trigonometrik funksiyalarni integrallash yevdoks knidskiy e.av. 408 — 355 yillar. integral hisob matematika rivojlanishining antik davrlariga borib taqaladi. qadimgi yunonistonda sirt va hajmlarni aniqlashning yevdoks knidskiy tomonidan ishlab chiqilgan ma’lum metodlari ba’zi sodda integrallarni hisoblash imkonini bergan leybnits gotfrid vilgelm (1646-1716) ∫ belgi leybnits tomonidan 1675 yilda kiritilgan. bu belgi lotin alifbosidagi s harfining o’zgartirilgan ko’rinishidir. (summa so’zidagi birinchi harf). gotfrid vilgelm leybnits (1646—1716) isaak nyuton (1643 – 1727) nyuton va leybnitslar bir - birlaridan bexabar ravishda integral uchun nyuton – leybnits formulasini ishlab chiqishdi. ostyugen luyi koshi (1789 – 1857) karl tedor vilgelm veyershtrass (1815 1897...

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