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The Gaussian integral

### Solution

Let, \(I=\int_{0}^{\infty} e^{-x^{2}} d x \;\;\;\;\;\;\; (1)\)

Also, \(I=\int_{0}^{\infty} e^{-y^{2}} d y \;\;\;\;\;\;\; (2)\)

\[\large \Rightarrow\int_{0}^{\infty} e^{-x^{2}} d x=\frac{\sqrt{\pi}}{2}\]

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Why does the number \(98\) disappear when writing the decimal expansion of \(\frac{1}{9801}\) ?

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