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This question already has an answer here:

I am pretty sure I have read the answer somewhere on this site, but sadly I am unable to find the question.

How to evaluate $\int_{-\infty}^\infty e^{-x^2} \mathrm{d}x$ using the residue theorem?

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marked as duplicate by Keba, Kamil Jarosz, Surb, Claude Leibovici, Davide Giraudo Jan 27 '16 at 11:51

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.