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

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

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integral from 0 to 1 of e^{(-x^2)}

\int_{0}^{1} e^{(- x^{2})} d x

0.74682 \dots

Solution steps

\int_{0}^{1} 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}^{1}

Compute the boundaries:

0.74682 \dots

= 0.74682 \dots

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