证设x∈(a,bΔx是增量,且x+Aw∈(an,b),则 Φ(x+△x) 于是 △Φ=Φ(x+△x)-d(x) y=f(x) f(dt-Cf()dt x+△x s x+Ar bx =f()(x+△x)-x](积分中值定理 f(s)mx (在x与x+Ax之间证 设x(a,b),x是增量,且x + x(a,b),则 + + = x x a (x x) f (t)dt 于是 = (x + x) − (x) + = − x x a x a f (t)dt f (t)dt = + − x + a x a x x x f (t)dt f (t)dt f (t)dt + = x x x f (t)dt = f ( )[(x + x) − x] = f ( )x (积分中值定理) (在x与x + x之间) (x) y = f (x) y 0 a x x + x b x f ( )