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Beliebt Rechnen >

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

Lösung

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

Lösung

2 π

+1

Dezimale

2.50662 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

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

= \frac{π}{2} - (- \frac{π}{2})

Vereinfache

= 2 π

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