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

The integral from 1 to infinity of e^{-x^2} is 0.13940…

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integral from 1 to infinity of e^{-x^2}

\int_{1}^{\infty} e^{- x^{2}} d x

0.13940 \dots

Solution steps

\int_{1}^{\infty} e^{- x^{2}} d x

Compute the indefinite integral:

\int e^{- x^{2}} d x = \frac{π}{2} erf (x) + C

Compute the boundaries:

\int_{1}^{\infty} e^{- x^{2}} d x = \frac{π}{2} - 0.74682 \dots

= \frac{π}{2} - 0.74682 \dots

Simplify

= 0.13940 \dots

y = x^{2}, x = y + 2, - 1, 2

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What is the integral from 1 to infinity of e^{-x^2} ?
The integral from 1 to infinity of e^{-x^2} is 0.13940…