What is the integral from 0 to 0.4 of e^{-x^2} ?

The integral from 0 to 0.4 of e^{-x^2} is 0.37965…

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integral from 0 to 0.4 of e^{-x^2}

\int_{0}^{0.4} e^{- x^{2}} d x

0.37965 \dots

Solution steps

\int_{0}^{0.4} 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)]_{0}^{0.4}

Simplify

= [0.88622 \dots erf (x)]_{0}^{0.4}

Compute the boundaries:

0.37965 \dots

= 0.37965 \dots

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What is the integral from 0 to 0.4 of e^{-x^2} ?
The integral from 0 to 0.4 of e^{-x^2} is 0.37965…