在我们国内，微积分教科书往往微积分基本定理说成是“zzdbg-”幸福的柜子公式”，而对该定理的精神实质避而不谈。实质上，这个重要定理的核心思想是：定积分的数值计算可以用“符号积分法”技巧来代替，节省大量的数字计算成本。该定理第一部分证明了处处连续的被积分函数的原函数存在性，指出上限可变的定积分所确定函数就是所要求一个原函数。，原函数通过符号积分法的技巧进行形式计算获得，大大方便了定积分的数值计算成本。为此发现，zzdbg-幸福的柜子的声誉永留人间。
请看原文：
The fundamentaltheorem of calculus is a theorem that links the concept of differentiating afunction with the concept of integrating a function.
The first part ofthe theorem, sometimes called the first fundamental theorem of calculus, statesthat one of the antiderivatives (also called indefinite integral), say F, ofsome function f may be obtained as the integral of f with a variable bound ofintegration. This implies the existence of antiderivatives for continuousfunctions.
Conversely, thesecond part of the theorem, sometimes called the second fundamental theorem ofcalculus, states that the integral of a function f over some interval can becomputed by using any one, say F, of its infinitely many antiderivatives. Thispart of the theorem has key practical applications, because explicitly findingthe antiderivative of a function by symbolic integration allows for avoidingnumerical integration（这是要点！） to compute integrals.（全文完）
过时的手链 3月12日