证 Vx, E[a,b],D(x)-(x,)= [, f(t)dt -[, f(t)dt= f(t)dt=F(5)(x-x)(在x,与x之间)Φ(x)-Φ(x).:. Φ'(x,)= limx-→>xox-xo= lim f()5→xo= f(x)
0 lim ( ) x f → = 0 = f x( ). 0 0 ( ) ( ) ( )d ( )d x x a a − = − x x f t t f t t 0 0 0 ( )d ( )( ) ( ) x x = = − f t t f x x x x 在 与 之间 0 0 0 0 ( ) ( ) ( ) lim x x x x x → x x − = − 0 证 x a b [ , ]
推论()是" f()dt=- (x); dr(x)(2)f(t)dt = f [p(x)]:p'(x);dxd) ()d(3)dr= f[b(x)]b'(x) - f [a(x)]a(x)
d ( ) (2) ( )d [ ( )] ( ); d x a f t t f x x x = ( ) ( ) d (3) ( )d d [ ( )] ( ) [ ( )] ( ). b x a x f t t x = − f b x b x f a x a x d (1) ( )d ( ); d a x f t t f x x = − 推论