integral from 1 to 4 of xe^{-x}

Lösung

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

- \frac{5}{e ^{4}} + \frac{2}{e}

Dezimale

0.64418 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

- \frac{5}{e ^{4}} + \frac{2}{e}

= - \frac{5}{e ^{4}} + \frac{2}{e}

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