aniq integralning tadbiqlari

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1. aniq integralning tadbiqlari i. aniq integral faraz qilaylik, y=f(x) funksiya biror [a,b] kesmada aniqlangan bo`lsin (a b bo`lsa 2. , 3. misol: ta’rifdan foydalanib , integralni hisoblang, bu yerda f(x)=x; a=0; b=1; yechish: [0,1] kesmani teng n ta bo`lakga bo`lamiz. u holda, har bir kesmaning uzunligi har bir da nuqta uchun kesmaning oxirini tanlaymiz, ya’ni integral yig`indini tuzamiz: shunday qilib, n’yuton – leybnis formulasi agar f(x) funksiya [a,b] kesmada uzluksiz f(x) funksiyaning biror boshlang`ich funksiyasi bo`lsa, u holda: (3) tenglik o`rinli bo`ladi. amaliy hisoblashlarda qulaylik uchun (3) formula quyidagicha ham yoziladi: (3) n’yuton – leybnis formulasi deyiladi. misollar: 1. 2. 3. 4. x 4 9 t 2 3 bu yerda: №1. aniq integralni hisoblang 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. №2 aniq integral yordamida quyidagi chiziqlar bilan chegaralangan shaklning yuzini toping. …
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xy = +-= 2 1 (1) 4 10 yx xy =- -+= i i i x x < < - x 1 n i , 1 = ( ) å d = n i i i n x f s x 0 max 1 ® d £ £ i n i x ò b a dx x f ) ( ò å d = = ® d b a i n i i x x f dx x f i 1 0 ) ( max lim ) ( x ò ò - = a b b a dx x f dx x f ) ( ) ( 0 ) ( = ò a a dx x f ò ò ò + = b c c a b a dx x f dx x f dx x f ) ( ) ( ) ( ò 1 0 xdx ú û ù …
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1. aniq integralning tadbiqlari i. aniq integral faraz qilaylik, y=f(x) funksiya biror [a,b] kesmada aniqlangan bo`lsin (a b bo`lsa 2. , 3. misol: ta’rifdan foydalanib , integralni hisoblang, bu yerda f(x)=x; a=0; b=1; yechish: [0,1] kesmani teng n ta bo`lakga bo`lamiz. u holda, har bir kesmaning uzunligi har bir da nuqta uchun kesmaning oxirini tanlaymiz, ya’ni integral yig`indini tuzamiz: shunday qilib, n’yuton – leybnis formulasi agar f(x) funksiya [a,b] kesmada uzluksiz f(x) funksiyaning biror boshlang`ich funksiyasi bo`lsa, u holda: (3) tenglik o`rinli bo`ladi. amaliy hisoblashlarda qulaylik uchun (3) formula quyidagicha ham yoziladi: (3) n’yuton – leybnis formulasi deyiladi. misollar: 1. 2. 3. 4. x 4 9 t 2 3 bu yerda: №1. aniq integralni hisoblang 1. 2. 3. 4. 5. …

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