The Dirichlet integral, given by ∫ from 0 to ∞ of (sin x / x) dx = π/2, is a fundamental result in mathematical analysis. This article presents detailed derivations using multiple methods, explores its convergence properties, generalized forms, and significant applications in Fourier analysis, signal processing, physics, and improper integral theory. The integral serves as a cornerstone connecting real analysis, complex analysis, and applied mathematics.
- Citation du texte
- Dr. Fazal Rehman (Auteur), 2026, The Dirichlet Integral and Its Applications in Mathematical Analysis, Munich, GRIN Verlag, https://www.grin.com/document/1722328