integral from 0 to 5 of xe^{-x/4}

Lösung

\int_{0}^{5} x e^{- \frac{x}{4}} d x

- \frac{36}{e ^{\frac{5}{4}}} + 16

Dezimale

5.68582 \dots

Schritte zur Lösung

\int_{0}^{5} x e^{- \frac{x}{4}} d x

Wende die partielle Integration an

= [- 4 e^{- \frac{x}{4}} x - \int - 4 e^{- \frac{x}{4}} d x]_{0}^{5}

\int - 4 e^{- \frac{x}{4}} d x = 16 e^{- \frac{x}{4}}

= [- 4 e^{- \frac{x}{4}} x - 16 e^{- \frac{x}{4}}]_{0}^{5}

Berechne die Grenzen:

- \frac{36}{e ^{\frac{5}{4}}} + 16

= - \frac{36}{e ^{\frac{5}{4}}} + 16

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