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

The integral from-2 to 2 of (e^{-x^2}) is 1.76416…

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integral from-2 to 2 of (e^{-x^2})

\int_{- 2}^{2} (e^{- x^{2}}) d x

1.76416 \dots

Solution steps

\int_{- 2}^{2} 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)]_{- 2}^{2}

Compute the boundaries:

1.76416 \dots

= 1.76416 \dots

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What is the integral from-2 to 2 of (e^{-x^2}) ?
The integral from-2 to 2 of (e^{-x^2}) is 1.76416…