integral from 0 to 1 of xe^{-x/2}

Lösung

\int_{0}^{1} x e^{- \frac{x}{2}} d x

- \frac{6}{e ^{\frac{1}{2}}} + 4

Dezimale

0.36081 \dots

Schritte zur Lösung

\int_{0}^{1} x e^{- \frac{x}{2}} d x

Wende die partielle Integration an

= [- 2 e^{- \frac{x}{2}} x - \int - 2 e^{- \frac{x}{2}} d x]_{0}^{1}

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

= [- 2 e^{- \frac{x}{2}} x - 4 e^{- \frac{x}{2}}]_{0}^{1}

Berechne die Grenzen:

- \frac{6}{e ^{\frac{1}{2}}} + 4

= - \frac{6}{e ^{\frac{1}{2}}} + 4

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