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

x y \frac{d y}{d x} + y^{2} = 2 x

x \to + 0 lim (\frac{1}{x})

y^{^{'}} - \frac{7}{x} y = \frac{y ^{5}}{x ^{5}}

e^{5 (t - 2)}

\frac{1}{3} π r^{2} h

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…