In order to solve the Gaussian integral $\int\limits_{-\infty}^{\infty} e^{-x^2}\,dx$, we set this value to $I$, square, and evaluate the following double integral in polar form ($I=\sqrt{\pi}$). Can this method of rotating a function $f:\mathbb{R}^1 \to \mathbb{R}^1$ around the $y$-axis and then taking the square root of the resultant volume be applied to any function? What are the criteria for this method to be applied, if applicable?
2026-03-29 23:42:48.1774827768
Application of Gaussian Integration Technique
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