Dirac delta function

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The Dirac delta function, $\delta (x)$ can be loosely defined as the function $\delta(x) = \begin{cases} + \infty ,\quad x = 0 \\ 0 ,\: \qquad x \ne 0 \end{cases}$ and it satisfy the equation $\displaystyle \int_{-\infty}^{\infty} \delta(x) \, dx = 1$ .