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:<math>= \int_{-\infty}^{\infty} e^{-x^2}dx </math>
:<math>= \int_{-\infty}^{\infty} e^{-x^2}dx </math>
where in the last line we used the fact that the function <math>e^{-x^2}</math> is even. The integral is called the Gaussian integral and has a well known value of <math>\sqrt\pi</math>.
where in the last line we used the fact that the function <math>e^{-x^2}</math> is an even function. The integral is called the Gaussian integral and has a well known value of <math>\sqrt\pi</math>.
Thus,
Thus,