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## Homework Statement

Consider the gaussian distribution shown below

[tex] \rho (x) = Ae^{-\lambda (x-a)^2 [/tex]

where A, a, and [itex] \lambda [/itex] are positive real constants. Use [itex] \int^{-\infty}_{+\infty} \rho (x) \,dx = 1 [/itex] to determine A. (Look up any integrals you need)

## Homework Equations

Given in question above

## The Attempt at a Solution

My plan was to integrate the probability density set it equal to one and then solve for A. The problem is I'm getting stuck on the integration. I started by pulling the constants out of the integral and doing the substitution [itex] u=x-a [/itex] that left me with

[tex] Ae^{-\lambda} \int^{+\infty}_{-\infty} e^{u^2}\,du [/tex]

It's been a while since calc II and I can't figure out how to do this one (even though it looks so simple). I also tried looking it up in a integral table but couldn't find it. Any help would be appreciated.