Integration of Trigonometric Functions Using Substitution Methods
Senior Grade Lecturer in Science, Government Polytechnic, Harapanahalli-583131, Karnataka India.
Research Article
World Journal of Advanced Research and Reviews, 2021, 11(01), 299-302
Publication history:
Received on 08 July 2021; revised on 19 July 2021; accepted on 26 July 2021
Abstract:
Integration of trigonometric functions is a core topic in differential and integral calculus with wide applicability in mathematics, physics, and engineering. Many trigonometric integrals encountered in practice are not directly integrable using standard antiderivative formulas and require systematic transformation techniques. Among these, substitution methods play a central role by simplifying complex integrands through appropriate changes of variables. This paper presents a structured study of substitution techniques applied to the integration of trigonometric functions, including elementary uuu-substitution, trigonometric substitution for radical expressions, and advanced transformations such as the tangent half-angle substitution. Emphasis is placed on the mathematical foundations, conceptual reasoning, and classical approaches established in pre-2020 literature. By highlighting the relationship between trigonometric identities and substitution strategies, the paper demonstrates how seemingly difficult integrals can be reduced to standard forms. The discussion aims to strengthen analytical understanding and provide a unified perspective on substitution methods as essential tools in trigonometric integration.
Keywords:
Trigonometric integration; Substitution method; Trigonometric substitution; Integral calculus; Change of variables; Trigonometric identities
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