证由函数f(X),g(X)∈R(),对区域Ω和函 数f(),g(X进行分割,代替,求和,取极限得 ∫f(x)d9=mn∑f(A2=1 g(X)dQ2=lin Q 如>8(g1=1g 由极限的运算法则,有 im∑af(5)+Bg(5)AO,= l am∑f(5O+Bim∑g(5g2=1+B1 2→>0由函数 f (X ) , g(X )R() , 对区域  和函 数 f (X) , g (X) 进行分割 , 代替 , 求和 , 取极限得 lim ( ) I , 1 0 i f n i i  f  = = →   由极限的运算法则，有  +  = = → n i i i i f g 1 0 lim [ ( )  ( )]  f g  I +  I  =   f (X)d  =   g(X )d lim ( ) I , 1 0 i g n i i g  = = →     + = → i n i i f 1 0  lim ( )    = = → i n i i g 1 0  lim ( )  证