- #1
FatPhysicsBoy
- 62
- 0
Homework Statement
We define [tex]I_{n} = \int_{-∞}^{∞}x^{2n}e^{-bx^{2}}dx[/tex], where n is a positive integer. Use integration by parts to derive:[tex]I_{n}=\frac{2n-1}{2b}I_{n-1}[/tex]
Homework Equations
Parts formula.
The Attempt at a Solution
So I'm just stuck here, I'm baffled and confused. Firstly if I take the second term [tex]e^{-bx^{2}}[/tex] as my dv term then I cannot integrate it which in itself I don't understand. Clearly I have a lacking fundamental knowledge of calculus, why are there some functions such as this that we cannot integrate normally? My confusion is furthered by if I take the same term as my u then I am allowed to differentiate it normally and I can carry out the integration by parts but I get In crop up again and I'm going to end up in an infinite loop integrating by parts...
Perhaps there is some trick or manipulation of the integral that I can use but it doesn't help the fact that I don't understand why the second term cannot be integrated etc.
Any help on this would be much appreciated.