Calculus 7 : return of \(\pi\)

Calculus Level 3

\[ \large \int_{-\infty}^{\infty} \dfrac{1}{e^{x^2}} \, dx \]

If the value of above integral is of the form \(\displaystyle \large \pi^{\frac{a}{b}}\), where \(a\) and \(b\) are coprime positive integers, find the value of \(a + b\).

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