Test LaTex 1. $$I = \int\limits_{ - \infty }^\infty {{e^{ - {x^2}}}dx}$$ With dollar signs 2. $I = \int\limits_{ - \infty }^\infty {{e^{ - {x^2}}}dx} $ With backticks 3. ` $$I = \int\limits_{ - \infty }^\infty {{e^{ - {x^2}}}dx}$$ ` on

Sums, Subscripts and Superscripts test (LaTeX)

$${{\sigma }^{2}}=\frac{1}{N}\sum\limits_{i=1}^{N}{{}}{{\left( {{x}_{i}}-\bar{x} \right)}^{2}}$$

Sums, Subscripts and Superscripts test (Microsoft Office equation converted to jpeg)

$$r^2$$

$$25\%$$

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Question:

Prove that:
$$\int\limits_{-\infty }^{\infty }{{{e}^{-{{x}^{2}}}}dx=\sqrt{\pi }}$$