integral from 0 to ln(2) of (x-1)e^{-x}

Lösung

\int_{0}^{l n (2)} (x - 1) e^{- x} d x

- \frac{1}{2} ln (2)

Dezimale

- 0.34657 \dots

Schritte zur Lösung

\int_{0}^{l n (2)} (x - 1) e^{- x} d x

Wende die partielle Integration an

= [- e^{- x} (x - 1) - \int - e^{- x} d x]_{0}^{l n (2)}

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

= [- e^{- x} (x - 1) - e^{- x}]_{0}^{l n (2)}

Multipliziere aus

- e^{- x} (x - 1) - e^{- x} : - e^{- x} x

= [- e^{- x} x]_{0}^{l n (2)}

Berechne die Grenzen:

- \frac{1}{2} ln (2)

= - \frac{1}{2} ln (2)

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