Function Naming for Probability Equation - Solving Homework Problem

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Homework Statement


I need to know the name of the function below. I know it has to do with probability but that's all I know.

\int _{-\infty} ^{\infty}e^{-x^2} dx

Homework Equations


The Attempt at a Solution

 
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I presume you mean \int e^{-x^2} dx. The function e^{-x^2} is the Gaussian function, and the integral is called the Gaussian integral.
 
Yeah a Gaussian so it's a type of Normal Distribution . The "type" meaning, a normal distribution with certain values for the parameters.

marlon
 
It seemed to have a different name though. It had like 3 or 4 words to it.
 
Ahhh cool. I found what I needed. Thanks to both of you!
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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