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.

Inequality proof

Integral inequality refers to an inequality that contains more than two integrals. When the integral interval is the same, the different integrals in the same integral interval are combined first, and the inequality is proved flexibly by using the integral mean value theorem according to the conditions satisfied by the integrand function.

When proving definite integral inequality, in order to get rid of the integral sign, we often consider using the integral mean value theorem. If the integrand function is the product of two functions, we can consider using the first or second integral mean value theorem.