性质1 b 1f(x)±g(x)x=,f(x)t士!,(x)k 证1(x)士g(x)h=lm∑几(5)士g)△ =lim∑f(5)A±limZ8(5)x1 f(x)dc±.g(x)d (此性质可以推广到有限多个函数作和的情况) ∫Σfx)=∑「(x)k i=1  b a [ f (x) g(x)]dx=  b a f (x)dx  b a g(x)dx . 证   b a [ f (x) g(x)]dx i i i n i =  f  g x = → lim [ ( ) ( )] 1 0    i i n i =  f x = → lim ( ) 1 0   i i n i  g x = → lim ( ) 1 0   =  b a f (x)dx ( ) .   b a g x dx （此性质可以推广到有限多个函数作和的情况） 性质1    = = = b a n i b a i n i f i x dx f x dx 1 1 [ ( )] ( )