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

Lösung

\int_{0}^{1} x^{2} e^{x - 1} d x

1 - \frac{2}{e}

Dezimale

0.26424 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} e^{x - 1} d x

Wende die partielle Integration an

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

\int 2 x e^{x - 1} d x = 2 (e^{x - 1} x - e^{x - 1})

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

Berechne die Grenzen:

1 - \frac{2}{e}

= 1 - \frac{2}{e}

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