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Help to solve an integral e^(-x^2)

Posted 9 years ago

i need to integrate this ecuation e^(-x^2)

5 Replies

You can calculate the Jacobian in Mathematica as

In[12]:= Det @ 
  D[{r Cos[\[Theta]], r Sin[\[Theta]]}, {{r, \[Theta]}}] // Simplify

Out[12]= r

since x = r * Cos[theta] and y = r * Sin[theta]

POSTED BY: Frank Kampas

There's a YouTube video on how to do the integral

POSTED BY: Frank Kampas

Yes,Jim Baldwin. I'm looking for how to solve this integral step by step but i think that is more complicated than i thought. Because i saw that i need to use the "Jacobian" and other kind of rules that i haven't seen yet. (Sorry for my bad english.It is not my first language)

Posted 9 years ago

Are you looking for steps to arrive at the answer or just the answer? If the latter, then I suspect you want to integrate using what Luis Ledesma wrote but from minus infinity to plus infinity which results in $\sqrt \pi$. (This integrand is proportional to the standard normal probability density so if there are other limits of integration needed, then you might want to look at the standard normal cumulative distribution function.)

Integrate[E^-x^2, {x, -Infinity, Infinity}]
POSTED BY: Jim Baldwin
Posted 9 years ago

you could use the command integrate with the following:

In[1]:= Integrate[E^-x^2, x]

Out[1]= 1/2 Sqrt[\[Pi]] Erf[x]

I hope to serve you for something that information

POSTED BY: Luis Ledesma
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