# 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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### Is the mentioned method appropriate to solve $\int_{-\infty}^{\infty}\frac{\sin x}{x}\, dx$? [duplicate]

The integral is, $$I=\int_{-\infty}^{\infty}\frac{\sin x}{x}\, dx$$ I know the answer would be $\pi$ and I know how to solve this using Feynman's method and Fourier transform. However I was trying ...
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### Finding a Hahn Decomposition involving a Dirac Measure

Let $(X,F,\mu)$ be a finite measure space, i.e. $\mu(X)<\infty$. And let $x\in X$, and let $\delta_x$ be the Dirac measure with respect to $x$, i.e. $\delta_x(E)=1$ if $x\in E$ and $\delta_x(E)=0$ ...
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### Continuity and Differentiability of Step function?

All Differentiable functions must be continous , But step function is differentiable and its derrivative is Dirac delta function, Step function actually is not continous But it have Derrivative , How ...
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### proof of Delta dirac sifting [closed]

I need to proof this expression : $\int_{-\infty}^\infty \delta(x-a)f(x) \, dx=f(a)$ Starting with this one: $\int_{-\infty}^\infty \delta(x)f(x) \, dx=f(0)$ Thanks in advance
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### Numerical integration with delta functions?

I would like to integrate the following numerically: $\int\limits_{-\infty}^{+\infty} \int\limits_{-\infty}^{+\infty} \delta(x^2+y^2-1) dx dy = \pi$ I could replace the dirac delta function with a ...