integral from 1 to 2 of x^2e^x

Lösung

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

2 e^{2} - e

Dezimale

12.05983 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

2 e^{2} - e

= 2 e^{2} - e