How is Math Applied in Quantum Physics through Standard Normal Distribution?

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TimeRip496
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-∞(e(-x2)/(x02)) dx =π0.5x0

How do you get this? Sorry my math sucks.
 
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The standard normal distribution has a density function [itex]f(x)=\frac{1}{\sqrt {2\pi}}e^{-\frac{x^2}{2}}[/itex] with [itex]\int_{-\infty}^{\infty}f(x)dx=1[/itex].

Make the appropriate change of variables and you get the equation you have.