integral from 0 to 3 of (x^2e^x)

Lösung

\int_{0}^{3} (x^{2} e^{x}) d x

5 e^{3} - 2

Dezimale

98.42768 \dots

Schritte zur Lösung

\int_{0}^{3} x^{2} e^{x} d x

Wende die partielle Integration an

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{3}

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{3}

Berechne die Grenzen:

5 e^{3} - 2

= 5 e^{3} - 2

\int_{- 2}^{0} (x^{3} - 3 x^{2} - 10 x) d x

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