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

The integral from-infinity to 0 of e^{-x^2} is (sqrt(pi))/2

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integral from-infinity to 0 of e^{-x^2}

\int_{- \infty}^{0} e^{- x^{2}} d x

\frac{π}{2}

Decimal

0.88622 \dots

Solution steps

\int_{- \infty}^{0} 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_{- \infty}^{0} e^{- x^{2}} d x = 0 - (- \frac{π}{2})

= 0 - (- \frac{π}{2})

Simplify

= \frac{π}{2}

\int x \cdot ln^{4} (x) d x

x \to 2 - lim (- \frac{1}{x - 2})

in v erse l a pl a ce \frac{16}{s ^{2} + 9}

\frac{\partial}{\partial y} (\frac{4 x}{y})

\frac{d}{d x} (- \frac{1}{2} x^{4})

What is the integral from-infinity to 0 of e^{-x^2} ?
The integral from-infinity to 0 of e^{-x^2} is (sqrt(pi))/2