integral from 0 to 2 of x^2e^{-2x}

Lösung

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

- \frac{13}{4 e ^{4}} + \frac{1}{4}

Dezimale

0.19047 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

= [- \frac{1}{2} e^{- 2 x} x^{2} + \frac{1}{4} (- 2 e^{- 2 x} x - e^{- 2 x})]_{0}^{2}

Berechne die Grenzen:

- \frac{13}{4 e ^{4}} + \frac{1}{4}

= - \frac{13}{4 e ^{4}} + \frac{1}{4}

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