Thursday, June 14, 2018

calculus - Showing that $int_{-infty}^{infty} exp(-x^2) ,mathrm{d}x = sqrt{pi}$





The primitive of $f(x) = \exp(-x^2)$ has no analytical expression, even so, it is possible to evaluate $\int f(x)$ along the whole real line with a few tricks. How can one show that $$ \int_{-\infty}^{\infty} \exp(-x^2) \,\mathrm{d}x = \sqrt{\pi} \space ? $$


Answer



Such an integral is called a Gaussian Integral


This link should help you out.


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