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

Posted 10 years ago
 i need to integrate this ecuation e^(-x^2)
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Posted 10 years ago
 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 10 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}] 
 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