# THE GAUSSIAN INTEGRAL - University of Connecticut

We will give multiple **proofs** of this result. (Other lists of **proofs** are in [4] and [9].) The theorem is subtle because there is no simple antiderivative for e 21 2 x (or e 2x2 or e ˇx). For comparison, Z 1 0 xe 1 2 x2 dxcan be computed using the antiderivative e 1 2 x2: this integral is 1. 1. First Proof: Polar coordinates

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