aniq integral va uni hisoblash

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1576504120.doc ( ) x f y = ] , [ b a n n x x x x x , , , , , 3 2 1 0 k ] , [ b a n 0 x a = n x b = ]. , [ , ], , [ ], , [ 1 2 1 1 0 n n x x x x x x - k ( ) x f y = ] , [ 1 0 x x ] , [ , 2 1 1 x x x ] , [ , 3 2 2 x x x 3 x ] , [ 1 n n x x - 1 x 2 x 3 x 4 x 5 x n x n x 0 x a = 1 x 2 x 3 x 4 x 5 x n x b = ( ) ( ) ( ) …

i i i n x f x g f dx x g x f 1 1 lim ] [ lim ] [ x x x ( ) ( ) ( ) ò ò å ± = d ± = ¥ ® b a b a i n i i n dx x g dx x f x g . lim 1 x ( ) ( ) ò ò - = b a a b dx x f dx x f . b a = ( ) . 0 = ò a b dx x f ( ) x f ] , [ b a b a d i x ( ) . 0 1 ³ d å = i n i i x f x ( ) ( ) . 0 lim 1 ò å ³ = d = ®¥ b a i n i i n dx x f …

p p p a a a = × = ÷ ø ö ç è æ × - × + = ò + + 2 1 0 2 . 4 1 1 dx x x ò ò ò + + + = + + 2 1 0 2 1 0 2 2 2 1 0 2 4 1 1 4 1 4 1 1 dx x dx x x dx x x , 4 1 2 t x = + u x = 2 , 2 = ю t , 1 = к t , 1 = ю u 0 = к u = + + + = + + ò ò ò 2 1 0 2 1 0 2 2 2 1 0 2 4 1 1 4 1 4 1 1 dx x dx x x dx x x = ï þ ï ý ü ÷ ÷ ø ö …

3 sin 3 1 3 sin 3 3 sin 3 1 , 3 cos 3 cos p p p p xdx x x x v dv xdx du dx u x xdx x ò 2 6 2 . sin p p dx x x ò ò ò = + × - = ï ï þ ï ï ý ü - = = = î í ì = = = 2 6 2 6 2 6 2 2 2 sin , sin sin p p p p p p ctgxdx ctgx x ctgx x dx v dv x dx du dx u x dx x x ò = - + = + = + - = 2 6 2 6 2 6 2 1 ln 1 ln 6 3 sin ln 6 3 p p p p p p p p x ctgxdx xctgx . 2 ln 6 3 2 ln …

amida ta teng elementar kesmalarga ajratamiz va berilgan funksiyaning ularga mos qiymatlarini topamiz: embed equation.3 u holda, integral yig`indining qo`shiluvchilari integral yig`indi quyidagicha bo`ladi: u holda, demak, kv. birl. 2. aniq integralning xossalari 1- xossa. har qanday o`zgarmas son uchun quyidagi tenglik o`rinli: (1) isboti: funksiyaning dagi integral yig`indisini qaraydik: demak, (1) tenglik o`rinli ekan. 2- xossa. o`zgarmas sonni integral belgisi oldiga chiqarish mumkin: (2) isboti: funusiyaning dagi integral yig`indisi uchun quyidagi o`rinlidir: shuning uchun demak, funksiya oraliqda integrallanuvchi bo`lib, (2) formula o`rinli ekan. 3-xossa. agar va funksiyalar oraliqda integrallanuvchi bo`lsa, ularning algebraik yig`indisi ham shu oraliqda integrallanuvchi bo`ladi, ya`ni: (3) isboti: 4-xossa. agar aniq integralning chegaralari o`zaro almashtirilsa, uning ishorasi qarama –qarshiga o`zgaradi: (4) isboti talabalarga havola qilinadi. 5-xossa. chegaralari o`zaro teng, ya`ni bo`lgan aniq integral nolga teng: (5) isboti talabalarga havola qilinadi. 6-xossa. agar fnksiya da musbat bo`lib, bo`lsa, quyidagi tengsizlik o`rinli bo`ladi: (6) isboti: oraliq ixtiyoriy elementar …

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1576504120.doc ( ) x f y = ] , [ b a n n x x x x x , , , , , 3 2 1 0 k ] , [ b a n 0 x a = n x b = ]. , [ , ], , [ ], , [ 1 2 1 1 0 n n x x x x x x - k ( ) x f y = ] , [ 1 0 x x ] , [ , 2 1 1 x x x ] , [ , 3 2 2 x x x 3 x ] , [ 1 n n x x - 1 x 2 x 3 x 4 x …

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