integral from 0 to 4 of x^2e^{-x}

Lösung

\int_{0}^{4} x^{2} e^{- x} d x

- \frac{26}{e ^{4}} + 2

Dezimale

1.52379 \dots

Schritte zur Lösung

\int_{0}^{4} x^{2} e^{- x} d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Berechne die Grenzen:

- \frac{26}{e ^{4}} + 2

= - \frac{26}{e ^{4}} + 2

\int_{1}^{2} x^{2} + 1 d x

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\int_{0}^{1} - x^{2} + 2 x d x