Feynman Integration Example 5 - Integral of sin(x)/x from 0 to infinity
Channel: The Feynman Technique
Date: 05/02/2024

https://www.youtube.com/channel/UCepKxh_j0SH2cw0nbY9FwZQ?sub_confirmation=1

In this video, we dive into the evaluation of the integral of sin(x)/x from 0 to infinity, a classic problem in calculus known for its application in various fields of mathematics and physics. We start by revisiting a related result for the integral of sin(ax)/x, then proceed to apply complex analysis techniques, specifically Euler's formula, to transform our integral into a more manageable form. The video methodically demonstrates the process of defining a new function to simplify the integral, differentiating under the integral sign, and then integrating back to find the original function. We conclude with the application of logarithmic identities and limits to arrive at the final result of pi/2, showcasing the power of complex analysis in solving real-valued integrals.