# $\int_{-1}^{1}\exp(-at^2)/t^2 dt$ using residue theorem

How to calculate $$\int_{-1}^{1}\frac{e^{-at^2}}{t^2}dt$$ where $a>0$, using residue theorem?

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$\rm{d}t$ of course – zar Oct 24 '12 at 22:52

## 2 Answers

$$\frac{e^{-at^2}}{t^2}$$ is not an integrable function in a neighbourhood of zero.

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To use the Residue Theorem, you must integrate the function on a piecewise smooth closed Jordan curve.

Also, you must find the Laurent series expression for your function.

Hint: exp(x) = 1 + x + (x^2)/2 + ...

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