Ⅱ.若点c不在内不妨设a<b<c,其他情形可类似证明, 则由1有∫(x)=(对+0(x /(xk=/(x)-.(x)=/(x)+!(x) 性质5若f(x)与g(x)在[ab上都可积,且∨x∈[a,b],均有 f(x)≤g(x)则‖f(x)x≤g(x)dty 证∫[(x)-g(x)k=im∑U()-8(5)△x≤0 ∫/x)hx-g(x)k≤0(xkg(xk4 Ⅱ. 若点 c不在内.不妨设 a<b<c, 其他情形可类似证明, 则由Ⅰ有 ( ) ( ) ( ) c b c a a b f x dx f x dx f x dx = +    ( ) ( ) ( ) ( ) ( ) b c c c b a a b a c f x dx f x dx f x dx f x dx f x dx =−=+      性质5 若ƒ(x)与g(x)在[a, b]上都可积, 且  x a b [ , ] , 均有 ( ) ( ) b b a a f x dx g x dx  则   f x g x ( ) ( ).  0 1 [ ( ) ( )] lim [ ( ) ( )] 0 n b i i i a i f x g x dx f g x    → = 证  − = −    ( ) ( ) 0 b b a a f x dx g x dx −    ( ) ( ) b b a a f x dx g x dx   