Evaluation Of Some Trigonometric Definite Integrals Using Contour Integration And The Residue Theorem:- Okechukwu Kanu

ABSTRACT Where a2 > b2 + c2 The second evaluates viii This project investigates the application of complex variable techniques in evaluating definite trigonometric integrals that are difficult to compute by ordinary calculus methods. The study introduces the basic concepts of analytic functions, contour integration, Cauchy's Integral Formula, Laurent series, singularities, and the Residue Theorem. These theoretical tools are then employed to evaluate two classes of definite integrals. The first establishes that de a + bcosd + csind 2n y/a2 — b2 — c2 r2n Jo using contour integration. The project demonstrates that complex analysis provides elegant and systematic techniques for evaluating real definite integrals.