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

This is the most common approach to this.

We square the integral, switch it to the product of 2 integrals in independent variables, and so use Fubini to create a double integral. That can then be switched to polar and actually evaluated.

switching to polar co-ordinates

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The integral of ( e^{-x^2} ) from negative infinity to positive infinity is equal to the square root of pi. It is commonly denoted as ( \sqrt{\pi} ).

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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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