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不定积分是积分学的基础,在教学过程中,须通过不定积分求原函数来计算定积分,因此学好不定积分是解决积分问题的基础知识,虽然定积分是积分学的关键,一元的定积分和多元的重积分,曲线积分、曲面积分以至泛函等问题,都是以定积分为必要知识,但如果学不好不定积分,则定积分无从学起,因此不定积分的重要性,是显而易见的,故教学中应该作为一个重点、不定积分教学不是很难的,但不能忽视的,是不定积分的求原函数问题,也就是不定积分的答案问题。 在微分学教学过程中,解出的结果一般是唯一的,故教学中习作的处理(即教师改作业)也比较容易,但不定积分则碰到答案(即原函数)形式常常是多样的,因此对学生的作业,必须逐步批阅,不能轻易决定其对或不对,这里提出答案中两种不同形式结果,供教学时参考。
Indefinite integrals are the basis of integralism. In the process of teaching, definite integrals must be calculated by using the original function of indefinite integrals. Therefore, learning indefinite integrals is the basic knowledge to solve the integral problem. Although definite integrals are the key to integralism, And multiple integrals such as multiple integrals, curve integrals, surface integrals, and even functional ones are all necessary integral knowledge. However, if you can not underestimate the integrals, you will not be able to learn definite integrals. Therefore, the importance of indefinite integrals is obvious Therefore, the teaching should be regarded as a key point, indefinite integral teaching is not difficult, but can not be ignored, is indefinite integral principle of the original function, that is, the problem of indefinite integral answer. In the course of differential teaching, the result of solving is generally unique. Therefore, it is relatively easy to deal with the teaching practice (that is, teachers change their homework), but the form of the answer (that is, the original function) Therefore, students’ homework must be gradually reviewed and can not be easily decided either right or wrong. Two different forms of results in the answer are presented here for reference in teaching.