Is there a proof that does not involve double integrals for proving normal pdf integrates to 1?
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1See some of the proofs in this website. http://www.math.uconn.edu/~kconrad/blurbs/analysis/gaussianintegral.pdf – Vivek Kaushik Sep 14 '17 at 03:32
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4Possible duplicate of Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \dfrac{\sqrt \pi}{2}$ – Chappers Sep 14 '17 at 03:38
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That question has plenty of methods, several of which don't use double integrals (the Wallis product one, for example). – Chappers Sep 14 '17 at 03:39