# 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 $\displaystyle \int_{-\infty}^{\infty} \delta(x) \, dx = 1$.

$\large \displaystyle\int _{ -\infty }^{ \infty }{ { e }^{ -{ x }^{ 2 } }\delta ({ x }^{ 2 }-2)\quad \, dx } =\dfrac { A{ e }^{ -B } }{ C\sqrt [ D ]{ F } }$

The equation above holds true for positive integers $A,B,C,D$ and $F$, find the minimum value of $A+B+C+D+F+2$.

**Notation**: $\delta(\cdot)$ denotes the Dirac delta function.

**Cite as:**Dirac delta function.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/dirac-delta-function/