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The integral de Fourier is a mathematical function used to calculate periodic functions. This video provides a complete explanation of the integral, including the definition and the necessary conditions for convergence. The author also explains the related Fourier transform function and how it can be used to analyze a sound wave in more detail.

**00:00:00**The video explains how to represent a function in terms of sines and cosines in the entire real line, but points out that it is not always possible to do so using a simple series. It then explains how to use an integral to do the same thing.**00:05:00**The integral of a function in an interval of the form ab, where ab is the length of the interval, can be calculated by parti rying that interval in n smaller intervals that partition it. The length of each small interval is called omega delta. Omega goes up by less omega go up by minus one, and the limit of the sum from k equal to one to n df of k times delta x can be found by multiplying up by pi and dividing by delta x.**00:10:00**The integral de Fourier is a useful tool for calculating periodic functions. This video provides a complete explanation of the integral, including the definition and the necessary conditions for convergence.**00:15:00**The integral of Fourier (or Fourier series) is a mathematical function that describes the extent to which a periodic function (e.g. a sound wave) repeats over a certain interval of time. In this video, the author explains its basic concept, and how it can be used to generate a graphical representation of a sound wave. He also mentions a related function called the Fourier transform, and how it can be used to analyze a sound wave in more detail. Finally, he thanks his viewers for their support on YouTube and on his other page, Jon Infinite.

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