METHODS THAT FACILITATE THE CALCULATION OF TRIGONOMETRIC INTEGRALS
Article Sidebar
Main Article Content
Abstract
Trigonometric integrals play a fundamental role in mathematical analysis and have extensive applications in physics, engineering, and other applied sciences. However, the direct evaluation of such integrals often involves considerable algebraic complexity, which necessitates the use of specialized analytical techniques. This article examines and systematizes methods that facilitate the calculation of trigonometric integrals, focusing on the application of trigonometric identities, substitution methods, integration by parts, reduction formulas, and exponential representations of trigonometric functions. The study highlights the conditions under which each method is most effective and demonstrates how appropriate method selection can significantly simplify the integration process. The results of the analysis emphasize the importance of a structured and methodological approach to trigonometric integrals in both theoretical and applied contexts. The findings may be useful for students, educators, and researchers seeking to improve analytical efficiency and deepen their understanding of integral calculus.
Article Details
References
1. Euler L. Introductio in analysin infinitorum. – Lausanne: Marc-Michel Bousquet & Co., 1748. – 2 vols.
2. Fourier J. Théorie analytique de la chaleur. – Paris: Firmin Didot, 1822. – 639 p.
3. Gradshteyn I. S., Ryzhik I. M. Table of Integrals, Series, and Products. – 8th ed. – Amsterdam: Academic Press, 2014. – 1184 p.
4. Apostol T. M. Calculus. Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra. – New York: John Wiley & Sons, 1967. – 666 p.
5. Stewart J. Calculus: Early Transcendentals. – 8th ed. – Boston: Cengage Learning, 2016. – 1368 p.
6. Jurakulova F. M. Solving trigonometric equations using methods of integrating trigonometric functions // Scientific Progress. – 2021. – No. 6. – URL: https://cyberleninka.ru/article/n/trigonometrik-tenglamalarni-trigonometrik-funksiyalarni-integrallash-usullaridan-foydalanib-yechish