integral from 0 to 1 of e^{-x}x

Lösung

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

- \frac{2}{e} + 1

Dezimale

0.26424 \dots

Schritte zur Lösung

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

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