integral from 1 to 2 of x*e^{-x}

Lösung

\int_{1}^{2} x \cdot e^{- x} d x

- \frac{3}{e ^{2}} + \frac{2}{e}

Dezimale

0.32975 \dots

Schritte zur Lösung

\int_{1}^{2} x e^{- x} d x

Wende die partielle Integration an

= [- e^{- x} x - \int - e^{- x} d x]_{1}^{2}

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

= [- e^{- x} x - e^{- x}]_{1}^{2}

Berechne die Grenzen:

- \frac{3}{e ^{2}} + \frac{2}{e}

= - \frac{3}{e ^{2}} + \frac{2}{e}

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