Darboux上、下积分 对a作分划序列 (n) (n) a=x0< (n) <x<∴<x (n) bn=12.3 7m)=max{x)-x:1≤i≤kn}lmn7m=0 n→>00 令(对每个及n) M(0)=sup((x):x≤xsx m,(n=inf(f(x): x 1Sx≤xm) Dmk积分f(xk=hm∑M"(x-x2 Darboux下积分cb f(x)x=im∑m1”( (n n→>00Darboux上、下积分 对[a,b]作分划序列 T (n) : a = x0 (n)  x1 (n)  x2 (n)  xk (n n ) = b n =1,2,3,  | | max{ : 1 } lim | | 0 ( ) ( ) 1 ( ) ( ) = −   = → − n n n n i n i n T x x i k T inf{ ( ): } sup{ ( ): } ( ) ( ) 1 ( ) ( ) ( ) 1 ( ) n i n i n i n i n i n i m f x x x x M f x x x x =   =   − − 令（对每个i及n） Darboux上积分 ( ) lim ( ) ( ) 1 ( ) 1 ( ) n i n i k i n i n b a f x dx M x x n − = → =  −  ( ) lim ( ) ( ) 1 ( ) 1 ( ) n i n i k i n i n b a f x dx m x x n − = → =  −  Darboux下积分 xi-1 xi