egri chiziqli integrallar. grin formulasi

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mavzu: egri chiziqli integrallar. grin formulasi reja: 1. to`g`ri to`tburchаklаr fоrmulаsi. 2. trаpеsiyalаr fоrmulаsi 3. simpsоn (pаrаbоlаlаr) fоrmulаsi 4. chеgаrаsi chеksiz bo`lgаn intеgrаl 5. chеgаrаlаnmаgаn (uzlukli) funksiyadаn оlingаn хоsmаs intеgrаl. 1. to`g`ri to`tburchaklar formulasi. kesmada aniqlangan va uzluksiz bo`lgan funksiyadan olingan integralni hisoblashni ko`raylik. kesmani nuqtalar bilan uzunliklari birxil, ya`ni bo`lgan n ta teng bo`laklarga ajrataylik. bo`lsin. endi funksiyaning nuqtalardagi qiymatlarini mos ravishda deb belgilab quyidagi yig`indilarni tuzaylik. va y d c y0 y1 y2 y3 yn 0 a=x0 x1 x2 b=xn x bu yig`indilarning har biri funksiya uchun kesmada tuzilgan integral yig`indi bo`ladi. shuning uchun integralning taqribiy qiymati (1) (2) (1) va (2) formulalar to`g`ri to`rtburchaklar formulasi deyiladi. chizmadan ko`rinadiki agar musbat va o`suvchi funksiya bo`lsa, u holda (1) formula ichki chizilgan to`g`ri to`rtburchaklardan tuzilgan zinapoyasimon shaklning yuzini tasvirlaydi. (2) formula esa tashqi to`rtburchaklardan tuzilgan zinapoyasimon shaklning yuzini tasvirlaydi. bu formulalar bilan hisoblanganda qo`yiladigan xatolik n soni qancha katta …

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gani uchun u y=f(x) d=an a2 a1 c 0 a=x0 x1 x2 xn=b x (3) (3) ga trapesiyalar formulasi deyiladi. misol. integralni n=5 da taqribiy hisoblang. yechish. = simpson (parabolalar) formulasi integralni taqribiy hisoblash talab qilinsin. buning uchun ni n=2m sondagi juft bo`lgan nuqtalar orqali bo`lakchalarga ajratib, f(x) funksiyaning bu nuqtalardagi qiymatlarini deylik. endi har bir oraliqga mos kelgan y= f(x) funksiya grafigini parabola yoyi bilan almashtiraylik. u holda egri chiziqli trapesiyaning yuzi taxminan yušoridan parabola yoylari bilan almashtirilgan bo`lakchalar yuzalarining yig`indisiga teng bo`ladi. yuqoridan parabola yoylari bilan chegaralangan shakllar yuzalarini hisoblab qo`shsak quyidagi formula kelib chiqadi: yoki n=2m bo`lgani uchun (4) (4) ga simpson yoki parabolalar formulasi deyiladi. misol. integralni n=2m=8 bo`lganda hisoblang. yechish. = demak simpson formulasidagi xatolik juda kam bo`lar ekan. eslatma. integralni (1) yoki (2) to`g`ri to`rtburchaklar formulasi yordamida taqribiy hisoblaganda quyidagi xatolik formula bilan hisoblanadi. bu yerda m1 ning kesmadagi eng katta qiymati. integralni (3) …

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holda xosmas integralni mavjud yoki yaqinlashuvchi deyiladi. agar - chekli limit mavjud bo`lmasa, u holda xosmas integralni mavjud emas yoki uzoqlashuvchi deyiladi. agar f(x)>0 desak xosmas integralning geometrik ma`nosi chiziqlar orasidagi cheksiz soha yuzini ifodalashi chizmadan ko`rinadi. хuddi shuningdek integralni ko`rsak = y x x=a 0 x=b agar xosmas integral ko`rinishda bo`lsa, u holda quyidagi ikkita xosmas integrallar yig`indisi sifatida qaraladi = + agar o`ng tomondagi xosmas integrallarning har biri mavjud bo`lsa, u holda chap tomondagi integral mavjud bo`ladi. misol. demak xosmas integral yaqinlashuvchi ekan. 2. chegaralanmagan (uzlukli) funksiyadan olingan xosmas integral f(x) funksiya oraliqda aniqlangan va uzluksiz bo`lib, uning har qanday qismida integrallanuvchi bo`lsin embed equation.3 f(x) funksiya x=b nuqtada aniqlanmagan yoki uzulishga ega. bu holda =f(c) integralni ko`rish mumkin. ta`rif. agar chekli limit mavjud bo`lsa, bu limitga f(x) funksiyaning oraliqdagi xosmas integrali deyiladi va = ko`rinishda yoziladi. y 0 x=a x=c x= x o`ng tomondagi limit mavjud bo`lsa, …

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o`lsa, integral ham uzoqlashuvchi bo`ladi. misol. ( o`zgarmas son). f(x)= funksiya x=0 nuqtada uzulishga ega = � embed equation.2 �� у= f (x) у=f(x) (x) _1405245068.unknown _1405245101.unknown _1405245117.unknown _1405245133.unknown _1405245141.unknown _1405245145.unknown _1405245149.unknown _1405245151.unknown _1405245153.unknown _1405245155.unknown _1405245156.unknown _1405245154.unknown _1405245152.unknown _1405245150.unknown _1405245147.unknown _1405245148.unknown _1405245146.unknown _1405245143.unknown _1405245144.unknown _1405245142.unknown _1405245137.unknown _1405245139.unknown _1405245140.unknown _1405245138.unknown _1405245135.unknown _1405245136.unknown _1405245134.unknown _1405245125.unknown _1405245129.unknown _1405245131.unknown _1405245132.unknown _1405245130.unknown _1405245127.unknown _1405245128.unknown _1405245126.unknown _1405245121.unknown _1405245123.unknown _1405245124.unknown _1405245122.unknown _1405245119.unknown _1405245120.unknown _1405245118.unknown _1405245109.unknown _1405245113.unknown _1405245115.unknown _1405245116.unknown _1405245114.unknown _1405245111.unknown _1405245112.unknown _1405245110.unknown _1405245105.unknown _1405245107.unknown _1405245108.unknown _1405245106.unknown _1405245103.unknown _1405245104.unknown _1405245102.unknown _1405245085.unknown _1405245093.unknown _1405245097.unknown _1405245099.unknown _1405245100.unknown _1405245098.unknown _1405245095.unknown _1405245096.unknown _1405245094.unknown _1405245089.unknown _1405245091.unknown _1405245092.unknown _1405245090.unknown _1405245087.unknown _1405245088.unknown _1405245086.unknown _1405245077.unknown _1405245081.unknown _1405245083.unknown _1405245084.unknown _1405245082.unknown _1405245079.unknown _1405245080.unknown _1405245078.unknown _1405245072.unknown _1405245074.unknown _1405245076.unknown _1405245075.unknown _1405245073.unknown _1405245070.unknown _1405245071.unknown _1405245069.unknown _1405245035.unknown _1405245051.unknown _1405245059.unknown _14052

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mavzu: egri chiziqli integrallar. grin formulasi reja: 1. to`g`ri to`tburchаklаr fоrmulаsi. 2. trаpеsiyalаr fоrmulаsi 3. simpsоn (pаrаbоlаlаr) fоrmulаsi 4. chеgаrаsi chеksiz bo`lgаn intеgrаl 5. chеgаrаlаnmаgаn (uzlukli) funksiyadаn оlingаn хоsmаs intеgrаl. 1. to`g`ri to`tburchaklar formulasi. kesmada aniqlangan va uzluksiz bo`lgan funksiyadan olingan integralni hisoblashni ko`raylik. kesmani nuqtalar bilan uzunliklari birxil, ya`ni bo`lgan n ta teng bo`laklarga ajrataylik. bo`lsin. endi funksiyaning nuqtalardagi qiymatlarini mos ravishda deb belgilab quyidagi yig`indilarni tuzaylik. va y d c y0 y1 y2 y3 yn 0 a=x0 x1 x2 b=xn x bu yig`indilarning har biri funksiya uchun kesmada tuzilgan integral yig`indi bo`ladi. shuning uchun integralning taqribiy qiymati (1) (2) (1) va (2) formulalar to`g`...

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