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:
\[\int\limits_{-\infty }^{\infty }{{{e}^{-{{x}^{2}}}}dx=\sqrt{\pi }}\]