# What is the integral of #e^(-x^2)#?

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The integral of ( e^{-x^2} ) with respect to ( x ) does not have an elementary antiderivative expressed in terms of standard mathematical functions. This integral is a well-known non-elementary function and cannot be expressed using elementary functions such as polynomials, exponentials, trigonometric functions, or their inverses. However, it does have significance in probability theory and statistics, particularly in the context of the Gaussian probability distribution function. The integral is denoted by ( \int e^{-x^2} dx ) and is often represented using the error function, denoted by ( \text{erf}(x) ).

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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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