Thermal Physics

Answers and Replies

  • #2
213
8
it's asking you to calculate

[tex] \int x^{2n} \textit{N}(x) dx [/tex]
 
  • #3
1,661
2
it's asking you to calculate

[tex] \int x^{2n} \textit{N}(x) dx [/tex]

Using induction? It looks like I can solve that integral with integration by parts.
 
  • #4
213
8
I suppose the inductive part comes from solving for the first few n and then coming up with a general n dependent solution. So yeah use integration by parts to find the first few moments. One can use the simpler method of observing that [tex] \int x^{2n}e^{-\alpha x^2} dx = (-1)^n \int \frac{\partial^{n}}{\partial \alpha^{n}} e^{-\alpha x^2} dx [/tex] and then using the standard results of a gaussian integral
 

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