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How do you find the antiderivative of #e^(-2x^2)#?

Answer 1

It doesn't have one, unless you allow the use of the error function #erf(x)# but that is a bit circular because the definition of #erf(x)# is #(2/sqrt(pi))int_-oo^x e^{-t^2}dt#.

A substitution like #x=t/sqrt(2)# looks like a good start.

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Answer 2

William Abdalla

To find the antiderivative of ( e^{-2x^2} ), you can use techniques like substitution or integration by parts. However, there isn't a simple closed-form expression for the antiderivative of this function using elementary functions. It involves special functions such as the error function. So, the antiderivative would be expressed as ( \frac{\sqrt{\pi}}{2\sqrt{2}} \text{erf}(x\sqrt{2}) + C ), where ( \text{erf}(x) ) is the error function and ( C ) is the constant of integration.

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Answer from HIX Tutor

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.