四、定积分的性质 (设所列定积分都存在) 1.f)d=-()df(x)dx=0 2.[dx=b-a 3.∫2kfe)de=k小2f(x)d :(k为常数) 4.∫fx)±g(x)]dx=-∫gfx)dr±∫g(x)d 证：左端=lim∑[f(5)±g(5]Axi 201 n =lim∑f(5;)△x,±lim∑g(5)△x,=右端 2→01 2→01 四、定积分的性质 (设所列定积分都存在) ( )d = 0  a a f x x  b a 2. dx ( k 为常数)     =  b a b a b a 4. [ f (x) g(x)]dx f (x)dx g(x)dx 证: i i i n i =  f  g x → = lim [ ( ) ( )] 1 0    左端 i i n i i i n i =  f x  g x → = → = lim ( ) lim ( ) 1 0 1 0     = 右端 = b − a