aniq integralning mexanika masalalariga tatbiqlari

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1576220402.doc ò = b a dx x m ) ( r å = = n i i i x y m m 1 å = = n i i i y x m m 1 m m m y m y m m m x m x x n i i n i i i ń y n i i n i i i ń = = = = å å å å = = = = 1 1 1 1 , )) ( ); ( ( ' ' i i i t y t x a ] ; [ 1 ' i i i t t t - î ) ( ' i t r ( ) n i a i ; 1 = i i i t t m d = ) ( ' r ) , 1 ( n i = ) ; ( y x å …

) sin ( )) cos 1 ( ( = = = + = ò ò ò p p p j j j j j j 0 0 2 0 | 2 cos 2 2 cos 2 2 cos 1 2 d a d a d a . 4 2 sin 2 2 2 cos 2 0 0 a a d a = ÷ ø ö ç è æ = = ò p p j j j ò ò = - = + = p p j j j j j j j j 0 2 2 2 0 2 cos ) 1 2 cos 2 ( 2 cos 2 . 2 2 cos 2 cos ) cos 1 ( d a d a a my ò = - = p j j j 0 2 2 2 ) 2 (sin ) 1 2 cos 2 ( 2 cos 2 . …

16 4 3 4 3 2 4 3 ) 2 ( 4 3 ) 2 ( 1 2 0 4 3 2 0 3 2 2 0 2 = × = ÷ ø ö ç è æ - = ÷ ÷ ø ö ç ç è æ - = - = - = ò ò x x x x x dx x x x s x = ÷ ø ö ç è æ + - = + - = - = ò ò 2 0 5 4 3 2 0 4 3 2 2 0 2 2 5 3 4 8 3 ) 4 4 ( 2 3 ) 2 ( 2 1 x x x dx x x x dx x x s y . 4 . 0 5 2 5 2 3 2 8 3 5 2 6 16 3 2 10 8 3 5 32 16 3 …

1 2 2 0 1 2 1 2 ) ( , , ds s y s x i ds s x i ds s y i s s y s x ò ò ò + = = = 0 2 2 0 0 2 0 2 )) ( ) ( ( , ) ( , ) ( r x r x r y £ £ - - = , 2 2 dx y r dx y ds y x x r x y = + = - = - - = 2 2 2 ' 1 , ' 3 2 0 2 2 2 2 2 2 4 2 2 r r r dx x r r dx x r r ydx r dx y r y i r r r r r r r x p p = × = - = - = = × = ò ò …

i m b a y y y y h dx x f 1 1 1 2 1 2 2 0 2 4 3 ) ( ò + 1 0 2 1 x dx 1 , 0 10 0 1 = - = - = n a b h 2 1 ш x + ( ) ; 8100 , 0 ) 1687 , 3 9311 , 3 000 , 1 ( 1 , 0 1 1 0 2 1 0 2 » + + = + + » + ò å å y h x dx ( ) ; 7600 , 0 ) 5000 , 0 1687 , 3 9311 , 3 ( 1 , 0 1 1 0 10 2 1 2 » + + = + + » + ò å å y h x dx ; 7850 , 0 1687 , 3 9311 , 3 2 5000 , …

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1576220402.doc ò = b a dx x m ) ( r å = = n i i i x y m m 1 å = = n i i i y x m m 1 m m m y m y m m m x m x x n i i n i i i ń y n i i n i i i ń = = = = å å å å = = = = 1 1 1 1 , )) ( ); ( ( ' ' i i i t y t x a ] ; [ 1 ' i i i t t t - î ) ( ' i t r ( ) n i …

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