The integral mean value theorem is a mathematical law. It is divided into the first mean value theorem of integral and the second mean value theorem of integral, each of which contains two formulas. Among them, the second mean value theorem of integral also contains three common inferences.

The mean value theorem of integrals reveals a method of transforming integrals into function values or complex functions into simple functions. It is a basic theorem and an important means of mathematical analysis, which is widely used in finding limits, judging some property points, estimating integral values and so on.

Extended data:

The integral mean value theorem plays an important role in application, which can remove the integral sign or make the complex integrand function become a relatively simple integrand function, thus simplifying the problem.

Therefore, when proving an equation or inequality containing functional integral in related problems, or when the conclusion to be proved contains definite integral, or when the limit formula to be proved contains definite integral, we should generally consider using the mean value theorem of integral, removing the integral symbol or simplifying the integrand function.

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