微积分第一基本定理和积分中值定理的新证法

New method to proof primacy fundamental theorem of differential coefficient and mean value theorem of integral

首先用Newton-Leibniz公式证明了微积分第一基本定理,然后又将变上限积分函数Φ(x)=∫xaf(t)dt在[a,b]上应用Lagrange中值定理,证明了积分中值定理,亦证明了积分中值定理的中间点与微分中值定理的中间点是相一致的,从而可使微积分教学更加灵活。

This paper coefficient, then draw first apply Newton- Leibniz formula to Lagrange mean value theorem on changing proof primacy fundamental theorem of differential the upper limit integral function Ф（x）= ∫a^xf（t）dt to proof mean value theorem of integral. Also proofed the midpoint of mean value theorem of integral and mean value theorem of differential coefficient is accordant, so these＇ methods can make the teaching of differential coefficient and integral flexible.