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Today Xiaobian brings you "Multivariate Functions: Exploring the Mysteries of the Multidimensional World", you are welcome to visit.
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定积分：微积分的基础和核心
Definite integral: The foundation and core of calculus
微积分是现代数学中的一个重要分支，它是研究函数的变化率和极值的数学分支。而定积分则是微积分的基础和核心，它是将一个区间内的函数值计算为一个定值的方法。
Calculus is an important branch in modern mathematics, it is the branch of mathematics that studies the rate of change and extreme values of functions.
定积分的基本思想是将一个区间内的函数值计算为一个定值，即将函数在该区间内的所有值都乘以一个固定的数值，然后将所有结果相加得到一个定值。这个定值就是函数在该区间内的定积分值。
Indefinite integration is the foundation and core of calculus, which is a method of calculating the value of a function in an interval into a fixed value.
定积分的应用非常广泛，它可以用于计算曲线的长度、平面图形的面积、旋转体的体积等。在工程领域中，定积分可以用于计算机械零件的质量、机器运行的速度等。在经济领域中，定积分可以用于计算股票价格、货币流通量等。
Definite integrals are widely used, and it can be used to calculate the length of curves, the area of planar figures, the volume of rotating bodies, etc. In engineering, definite integrals can be used to calculate the quality of mechanical parts, the speed at which machines run, etc. In the economic field, definite integrals can be used to calculate stock prices, money circulation, etc.
定积分的计算方法非常简单，它只需要将函数在区间内的所有值都乘以一个固定的数值，然后将所有结果相加得到一个定值即可。但是，定积分的计算需要掌握一定的数学知识和技巧，如微积分、极限等。
The calculation method of definite integration is very simple, it only needs to multiply all the values of the function in the interval by a fixed value, and then add all the results together to get a fixed value. However, the calculation of definite integrals requires certain mathematical knowledge and skills, such as calculus, limits, etc.
总之，定积分是微积分的基础和核心，它是将一个区间内的函数值计算为一个定值的方法。它的应用非常广泛，它可以用于计算曲线的长度、平面图形的面积、旋转体的体积等。通过学习定积分，我们可以更好地理解微积分中的复杂概念，并让计算机更好地理解和处理人类语言。
In short, definite integration is the foundation and core of calculus, which is a method of calculating the value of a function in an interval as a fixed value. It has a wide range of applications, it can be used to calculate the length of curves, the area of flat figures, the volume of rotating bodies, etc. By learning definite integrals, we can better understand complex concepts in calculus and allow computers to better understand and process human language.
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参考资料：百度百科-秒懂百科、《高等数学辅导及习题精解》、《高等数学第七版上册》
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