Скачать или смотреть How to Integrate Riemann’s Function — A Rigorous Step-by-Step Derivation

In this video, we study the integration of Riemann’s function defined by a highly oscillatory trigonometric series. Our goal is to compute the definite integral of this function over an arbitrary interval [x1, x2].We begin by justifying the interchange of summation and integration using the Weierstrass M-test and uniform convergence. Then we carefully perform the term-by-term integration and derive the final result.


Timecode:
00:00 — Intro
00:24 — Problem & Solution: Defining and Integrating R(x)
04:58 — Geometric interpretation (Riemann’s function)


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