# What is #int_-oo^oo e^(-x^2)dx#?

This non-elementary function is suitably scaled so that:

So

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The integral of (e^{-x^2}) from negative infinity to positive infinity is equal to the square root of pi ((\sqrt{\pi})). This result is a fundamental part of the Gaussian integral, which has various applications in probability theory, statistics, and physics.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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