Artificial intelligence

Abstract: Two mean value theorems in the integral calculus have been considered in the article. The first theorem is an integral analogue of the Cauchy’s theorem from differential calculus. The second one is a generalization of the Cauchy’s first theorem. These theorems expend our imagination about the function mean value. The mean value concept is a function mean value with respect to the other function. The third integral mean value theorem can be used for estimation of some definite integrals.

Keywords: : integral, mean value theorem, generalized theorem, function mean value, integral measure, average value

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