integral from 0 to 10 of xe^{-x/(12)}

Lösung

\int_{0}^{10} x e^{- \frac{x}{12}} d x

- \frac{264}{e ^{\frac{5}{6}}} + 144

Dezimale

29.26607 \dots

Schritte zur Lösung

\int_{0}^{10} x e^{- \frac{x}{12}} d x

Wende die partielle Integration an

= [- 12 e^{- \frac{x}{12}} x - \int - 12 e^{- \frac{x}{12}} d x]_{0}^{10}

\int - 12 e^{- \frac{x}{12}} d x = 144 e^{- \frac{x}{12}}

= [- 12 e^{- \frac{x}{12}} x - 144 e^{- \frac{x}{12}}]_{0}^{10}

Berechne die Grenzen:

- \frac{264}{e ^{\frac{5}{6}}} + 144

= - \frac{264}{e ^{\frac{5}{6}}} + 144

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