,
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 ] .