Thermal Physics: Understanding Heat and Energy Transfer

[Shackleford]

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png?t=1297136986

Huh?

Its sum is 1.

 

[sgd37]

it's asking you to calculate

$$\int x^{2n} \textit{N}(x) dx$$

 

[Shackleford]

it's asking you to calculate

$$\int x^{2n} \textit{N}(x) dx$$

Using induction? It looks like I can solve that integral with integration by parts.

 

[sgd37]

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 $$\int x^{2n}e^{-\alpha x^2} dx = (-1)^n \int \frac{\partial^{n}}{\partial \alpha^{n}} e^{-\alpha x^2} dx$$ and then using the standard results of a gaussian integral