integral from 0 to 1 of x^2sqrt(e^x)

Lösung

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

10 e - 16

Dezimale

0.48721 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [2 e^{\frac{x}{2}} x^{2} - \int 4 e^{\frac{x}{2}} x d x]_{0}^{1}

\int 4 e^{\frac{x}{2}} x d x = 16 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}})

= [2 e^{\frac{x}{2}} x^{2} - 16 (\frac{1}{2} e^{\frac{x}{2}} x - e^{\frac{x}{2}})]_{0}^{1}

Berechne die Grenzen:

10 e - 16

= 10 e - 16