# Questions tagged [dirac-delta]

This tag is for questions involving the Dirac delta function, either in the informal sense, or in the distribution sense. The Dirac delta function is a mathematical construct which is called a generalized function or a distribution and was originally introduced by the British theoretical physicist Paul Dirac.

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### Integral evaluation with delta Dirac

I am having doubts about the following integral:$$\int \limits _{0}^{10} \int \limits _{0}^{10} \frac{x^2y^2}{(x^2+y^2)^{5/2}}\ \delta(x)\ \mathrm{d}x\mathrm{d}y$$ If we apply the definition of the ...
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### Dirac Delta and its evaluation in a complicated integral

I would like to better understand how to use and manipulate the Dirac Delta function. It seems to me that whenever the delta function appears in an integral, it reduces the dimension of the domain of ...
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### I am evaluating the fourier transform of a function + a constant: $\frac{1}{2\pi}\int_{-\infty}^{+\infty}(f(x)+c)e^{-ikx}dx$ equals what?

I am evaluating the fourier transform of a function plus a constant $c$: $$\frac{1}{2\pi}\int_{-\infty}^{+\infty}(f(x)+c)e^{-ikx}dx.$$ As a result, I should get the fourier transform of the function ...
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### Fourier transform of delta(dirac) function-multiplication with exp function

I am trying to find an integral of multiplication exponential function with a delta function. I know a property of delta function that if I would like to take the integral of the multiplication delta ...
The next functions are defined: $$f(y)=\frac{1}{1+e^{-2y}} \\ g_1(z)=\frac{1}{1+z^2},\quad g_2(z)=e^{-z^2},\quad g_3(z)=\frac{1}{cosh(z)},\quad g_4(z)=\frac{sin(z)}{z}$$ Is there a way to calculate ...