(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The context of this question is physics related but the problem I am having is purely mathematical.

g(t)= e^(-(a^2)(t^2))*e^(iwt) (a and w are just constants, i is sqrt(-1), not a constant)

I need to integrate this function with respect to t from -infinity to +infinity.

2. Relevant equations

error function: erf(x) = 2/sqrt(pi) * e^-t^2dt evaluated from t=0 to t=x

erf(infinity)=1, erf(-infinity) = -1

3. The attempt at a solution

i simplified g(t) to = e^(iwt-(a^2)(t^2)) and used an online integrator to get the answer.

My problem is that the integrated function involves the error function. From the math classes I have taken, the only way for me to have gotten that answer is if I had looked it up.

Clearly I wont be able to use an online integrator on an actual test so I was wondering If there are methods to deduce the answer without actually taking the integral.

Any insight is much appreciated.

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# Homework Help: Need help integrating a function involving e^(-t^2)

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