一、从微分中值定理认识定积分的概念 定积分的概念,在现行各种教科书中,多是直接给出。然后,回过来证明定积分与不定积分的关系。于是,就有牛顿—莱布尼兹公式。这种方法,实际上是认识过程的一个逆序。由于这种逆序,往往给初学者理解定积分概念带来一定的困难。如能变换方式,从已学的知识中,直接推导出这个定积分概念,确有化难为易的好处。 1. Understanding the Concept of Definite Integral from the Differential Mean Value Theorem The concept of definite integral is given directly in many current textbooks. Then, back to prove the relationship between the definite integral and indefinite integral. So there is the Newton-Leibniz formula. This method is actually a reverse of the cognitive process. Because of this reverse order, it often gives beginners a certain degree of difficulty in understanding the concept of definite integration. If we can change the way, from the knowledge we have learned, we can directly derive the concept of this definite integral, which has the benefit of being difficult to change.