Definite Integral定积分
An integral for which the limits of integration are specified is called a definite integral. The value of this integral is completely specified by performing the integration and substituting the values of the limits. This is in contrast to an indefinite integral which has no specified limits.
积分的上下限已指定的积分称为定积分。该积分的值完全由进行积分并代入上下限的值来确定。这与不定积分形成对比，不定积分没有指定的上下限。 |
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Indefinite Integral不定积分
An indefinite integral or antiderivative has no specified limits for the integration. For application to specific problems, boundary conditions must be applied to the result in order to arrive at a specific value for the integral. The uncertainty in the value of the indefinite integral is expressed in the form of a constant of integration which is not defined by the integration process. The constant of integration is determined by applying the relevant boundary conditions to the problem. 不定积分或原函数没有指定的积分限。为了应用于具体问题，必须将边界条件应用到结果中，以得到积分的具体值。不定积分的值的不确定性以积分常数的形式表达，该常数不由积分过程定义。通过将相关边界条件应用到问题中来确定积分常数。
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Constant of Integration积分常数
The use of a constant of integration is a way to give a general result for an indefinite integral which arises in a physical problem. The process of integration does not give a specific value for the integral, but the application of physical boundary conditions makes possible the assigning of a definite value to the constant of integration, thereby fitting the calculation to the specific physical situation. 在物理问题中使用积分常数是一种方法，用于给出不定积分的一般结果。积分过程本身不会给出积分的具体值，但通过应用物理边界条件，可以给定积分常数一个确定的值，从而使计算符合具体的物理情况。 |
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