x+△v f(td+」f(o)dt-Jf()t x+△r f(t)dt 由积分中值定理得 Φ(x) xEx+△Cbx △①=f(引)△xξ∈x,x+△xl △Φ △Φ ∫(5),lim m∫( △x→>0△x△x->0 △x→>0,5→x Φ(x)=f(x) f t dt f t dt f t dt x a x x x x = a +  −  + ( ) ( ) ( ) ( ) ,  + = x x x f t dt 由积分中值定理得  = f ( )x [x, x + x], x → 0, → x f ( ), x =   lim lim ( ) 0 0 f  x→ x x→ =   (x) = f (x). a b x y o x + x (x) x