integral from 0 to a of x^2e^x

Lösung

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

a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

= a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

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a re a y = \frac{1}{16 x ^{2}}, y = x, y = \frac{x}{18}

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