integral from 5 to infinity of xe^{-x/2}

Lösung

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x

\frac{14}{e ^{\frac{5}{2}}}

Dezimale

1.14918 \dots

Schritte zur Lösung

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x

Berechne das unbestimmte Integral:

\int x e^{- \frac{x}{2}} d x = - 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}} + C

Berechne die Grenzen:

\int_{5}^{\infty} x e^{- \frac{x}{2}} d x = 0 - (- \frac{14}{e ^{\frac{5}{2}}})

= 0 - (- \frac{14}{e ^{\frac{5}{2}}})

Vereinfache

= \frac{14}{e ^{\frac{5}{2}}}

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