What is the integral from 0 to 1 of e^{-z^2} ?

The integral from 0 to 1 of e^{-z^2} is 0.74682…

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integral from 0 to 1 of e^{-z^2}

\int_{0}^{1} e^{- z^{2}} d z

0.74682 \dots

Solution steps

\int_{0}^{1} e^{- z^{2}} d z

Use the nonelementary integral:

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

= [\frac{π}{2} erf (z)]_{0}^{1}

Compute the boundaries:

0.74682 \dots

= 0.74682 \dots

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What is the integral from 0 to 1 of e^{-z^2} ?
The integral from 0 to 1 of e^{-z^2} is 0.74682…