The Dirichlet integral is a well-known result in analysis that deals with integrating an oscillating function over an infinite range. Despite the function’s continuous oscillations, the integral converges to a finite value, which was surprising when first discovered. This property is important in harmonic analysis and signal theory, showing how oscillatory behavior can produce meaningful averages over large intervals. 📌Support us - Like/Share/Follow👆❤️ ✅Follow @math.magazine 🔥 for more !!...
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Math Animations on Instagram: "The Dirichlet integral is a well-known result in analysis that describes the integration of the function sin(x)/x over the entire positive range. An elegant proof of this integral is provided by Fubini’s theorem, which allows the order of integration to be swapped in a multidimensional integral. In the case of the Dirichlet integral, we consider a two-dimensional function that is integrated over a rectangle in the first quadrant. By cleverly changing the order of i
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