89178030-9d9b-4ceb-8387-7c304e3c672820210312084412912wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON COMPUTERS1109-275010.37394/23205http://wseas.org/wseas/cms.action?id=40262720202720201910.37394/23205.2020.19http://wseas.org/wseas/cms.action?id=23186On the Comparison of Gauss and Hybrid Methods and their Application to Calculation of Definite IntegralsMehribanİmanovaComputational Mathematics, Baku State University, Institute of Control Systems named after Academician A. Huseynov, Executive Director, Science Development Foundation under the President of the Republic of Azerbaijan, Baku, AZERBAIJANAs is known there is the wide class of methods for calculation of the definite integrals constructed by the well-known scientists as Newton, Gauss, Chebyshev, Cotes, Simpson, Krylov and etc. It seems that to receive a new result in this area is impossible. The aim of this work is the applied some general form of hybrid methods to computation of definite integral and compares that with the Gauss method. The generalization of the Gauss quadrature formula have been fulfilled in two directions. One of these directions is the using of the implicit methods and the other is the using of the advanced (forward-jumping) methods. Here have compared these methods by shown its advantages and disadvantages in the results of which have recommended to use the implicit method with the special structure. And also are constructed methods, which have applied to calculation of the definite integral with the symmetric bounders. As is known, one of the popular methods for calculation of the definite integrals with the symmetric bounders is the Chebyshev method. Therefore, here have defined some relations between of the above mentioned methods. For the application constructed, here methods are defined the necessary conditions for its convergence. 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