用泰勒公式推导微积分的泊松基本定理
Poisson's fundamental theorem of calculus via Taylor's formula
摘要：
我们使用泰勒公式与拉格朗日余项作出现代适应的泊松证明的版本的基本定理的微积分的情况下，积分定义的欧拉和，即黎曼和左（或右）端点是等距的。我们讨论了这种方法在基础微积分课程的潜在好处。
英文摘要：
We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is defined by Euler sums, that is Riemann sums with left (or right) endpoints which are equally spaced. We discuss potential benefits for such an approach in basic calculus courses.
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