Г., кандидат технических наук, доцент Московского гуманитарно-экономического университета ИНТЕГРАЛЬНЫЕ ТЕОРЕМЫ О СУЩЕСТОВАНИИ РЕШЕНИЙ ЧИСЛОВЫХ УРАВНЕНИЙ Сформулированы и доказаны интегральные теоремы о существовании решения числовых уравнений с одним и многими неизвестными. <...> Galkanov A.G., candidate of technical science, the senior lecturer of chair of higher mathematics of the Moscow State humanitarian and economic University INTEGRAL THEOREMS ABOUT EXISTENCE OF THE SOLUTION OF THE NUMERICAL EQUATIONS Integral Theorems of existence of a solution for the numerical equations with one and many unknown are formulated and proved. <...> Let's consider the numerical equation f xg x Let () , f xdx g xdx Riemann's integrals. <...> At what values of parameters the solution on segment [0; 1]? <...> To apply the theorem of an average to n multiple integrals. <...> The Theorem 1 and its generalization (3) are most effective at research of the equations with sin . multiple integrals of Riemann. <...> At what values of parameters ,, ,ab and c existence of a solution of the 2 cos x account x [0; 2] we have Decision. <...> Galkanov A.G. The numerical equations and identities in concepts, theorems, methods, tasks and solutions (in Russian). – M.: MSF University publishing house, 2013. – 317 pages. 138 1 1 2 2 Proof. <...> The integral Theorem 2 can be applied and in problems of mechanics. <...>