What is the integral from-3 to 3 of e^{-x^2} ?

The integral from-3 to 3 of e^{-x^2} is 1.77241…

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integral from-3 to 3 of e^{-x^2}

\int_{- 3}^{3} e^{- x^{2}} d x

1.77241 \dots

Solution steps

\int_{- 3}^{3} e^{- x^{2}} d x

Use the nonelementary integral:

\int e^{- x^{2}} d x = \frac{π}{2} erf (x)

= [\frac{π}{2} erf (x)]_{- 3}^{3}

Compute the boundaries:

1.77241 \dots

= 1.77241 \dots

What is the integral from-3 to 3 of e^{-x^2} ?
The integral from-3 to 3 of e^{-x^2} is 1.77241…