积分学理论与应用的改革
首发时间:2012-01-09
摘要:使用求极限的"夹逼准则"可以证明:连续函数 构成的曲边梯形的面积函数是 的一个原函数。 解定积分应用问题的实质是先求出所求量函数的导数或微分,然后使用原函数增量方法解决的。将定积分定义为原函数的增量,可以使积分学理论大大地简化。
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Reformation on Theory and Applications of Integration
Abstract:Appling the squeeze rule may prove that the area function of trapezoid with curved edge constituted by continuous function is one primitive function. The nature of method to solve questions of definite integral is the method to count firstly derivative or differential of function calculated quantity, and to count finally increasing quantity of function calculated quantity. To definite the definite integral as increasing quantity of primitive function may simplify theory of integration greatly.
Keywords: Area function of trapezoid with curved edge Primitive function Integration element
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