integral from 0 to 1 of (xe^{-x})

Lösung

\int_{0}^{1} (x e^{- x}) d x

- \frac{2}{e} + 1

Dezimale

0.26424 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int - e^{- x} d x = e^{- x}

= [- e^{- x} x - e^{- x}]_{0}^{1}

Berechne die Grenzen:

- \frac{2}{e} + 1

= - \frac{2}{e} + 1

\int_{0}^{\frac{1}{3}} 2 (1 - x) d x

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