integral from 1 to 4 of e^{-x}(x-1)

Lösung

\int_{1}^{4} e^{- x} (x - 1) d x

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

Dezimale

0.29461 \dots

Schritte zur Lösung

\int_{1}^{4} e^{- x} (x - 1) d x

Wende die partielle Integration an

= [- e^{- x} (x - 1) - \int - e^{- x} d x]_{1}^{4}

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

= [- e^{- x} (x - 1) - e^{- x}]_{1}^{4}

Multipliziere aus

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

= [- e^{- x} x]_{1}^{4}

Berechne die Grenzen:

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

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

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