integral from 0 to 1 of 10x^2e^x

Lösung

\int_{0}^{1} 10 x^{2} e^{x} d x

10 (e - 2)

Dezimale

7.18281 \dots

Schritte zur Lösung

\int_{0}^{1} 10 x^{2} e^{x} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{0}^{1} x^{2} e^{x} d x

Wende die partielle Integration an

= 10 [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{1}

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

= 10 [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{1}

Berechne die Grenzen:

e - 2

= 10 (e - 2)

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