The mean value theorem of integral is a mathematical law, which is divided into the first mean value theorem of integral and the second mean value theorem of integral, each of which contains two formulas, and 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.

Application:

The integral mean value theorem plays an important role in application, which can remove the integral sign or change the complex integrand function into a relatively simple integrand function, thus simplifying the problem. Therefore, when proving an equation or inequality with a function integral in related problems, or the conclusion to be proved contains definite integral, or the obtained limit formula contains definite integral, we should generally consider using the mean value theorem of integral, removing the integral symbol or simplifying the integrand function.