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:




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.




,

 

1. l .

. , , . , . . l, [0, l ]. Î[0, l ], r(). [0, l ] D li, i = 1,..., n.

 

 

, , D li . x i D li , r(x i). mir(x i)D li, , D li (.. ).

2. , y = f (x), = = b [ a, b ] .(.1).

. [ a, b ] 1, 2,..., , D i [ xi 1, xi ].

 

 

 


D i f (x i), x i [ xi 1, xi ].

, D i. , .

, , : . , , , . .

.

 

y = f (x) [ a, b ]. [ a, b ]

= 0 < x 1 < x 2 <... < xn = b.

. [ xi 1, xi ] D i, .. D i = xi xi 1, l ,.. l = . [ xi 1, xi ] x i f (x i). , f (), x i. ¥ l 0, .

19.1. l 0, , x i, f () [ a, b ] .

f () , f () dx , , [ a, b ] , a, b : a , b .

, . f () [ a, b ].

, . f () a b, , .. = = =....

, :

l = b a, r = f (x), f (x) ³ 0, ;

, = f (x), f (x) ³ 0, = = b [ a, b ] .

[ a, b ], . .

19.1.( )

f (x) [ a, b ], .

, , ,

[ a, b ], , .. x i.

19.2.( )

1) [ a, b ], .

2) [ a, b ] (- ), .

3) [ a, b ] .





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