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

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

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

\int_{0}^{1} \frac{1}{e ^{x^{2}}} d x

0.74682 \dots

Solution steps

\int_{0}^{1} \frac{1}{e ^{x^{2}}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{x^{2}}} = e^{- x^{2}}

= \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

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