The methodology of teaching of the integration techniques of the rational functions by using partial fraction decomposition method and integration of the trigonometric functions

The problems introduced in the article here are the application problems from Mathematics and Engineering Sciences. All presented problems are unabridged and never published problems developed by the author for Pre-Calculus, Calculus and Differential Calculus subjects developed by the author during his teaching years at the colleges in USA. These unabridged problems are developed within the new trends in the evolutions of novelty of the syllabi in Mathematics due to the fast-pacing development of the Mathematics Sciences/ Theory and Applications. These new trends in the Theory and Application of Mathematics Sciences have been added new demands to the newly revised textbooks and corresponding syllabi for the Mathematics Courses taught at the Junior two years Colleges and Universities. There are introduced newly generated unabridged problems with the topics such as (a) Integration by partial fractions, (b) Integration of trigonometric functions and (c) Reduction formulas for the integration. These newly developed problems are reflection of the Development of Mathematical and Engineering Sciences to offer great amount of learning conclusion/sequel to those who pursue a bachelor’s degree at the universities. The problems presented in the article here are developed and restructured in terms of the newly developed techniques to solve the problem in Infinite Mathematics and Engineering sciences. Moreover, the techniques offered in the article here are more likely to get utilized in Advanced Engineering Sciences, too within the problems, which require to obtain finite numerical solutions to the Real Phenomena Natural Problems in Engineering Sciences and Applied Problems in Mathematical Physics.

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