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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{π}{2}

+1

Dezimale

1.25331 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int e^{\frac{- x ^{2}}{2}} d x = (\frac{π}{2})^{\frac{1}{2}} erf (\frac{x}{2}) + C

Berechne die Grenzen:

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

= \frac{π}{2} - 0

Vereinfache

= \frac{π}{2}

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