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

The integral from x to infinity of e^{-y^2} is (sqrt(pi)-sqrt(pi)\erf(x))/2

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

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

\frac{π - π erf ( x )}{2}

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{x}^{\infty} e^{- y^{2}} d y = \frac{π}{2} - \frac{π}{2} erf (x)

= \frac{π}{2} - \frac{π}{2} erf (x)

Simplify

= \frac{π - π erf ( x )}{2}

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What is the integral from x to infinity of e^{-y^2} ?
The integral from x to infinity of e^{-y^2} is (sqrt(pi)-sqrt(pi)\erf(x))/2