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Beliebt Rechnen >

integral from 0 to 1 of (9x)/(e^{2x)}

Lösung

\int_{0}^{1} \frac{9 x}{e ^{2 x}} d x

Lösung

9 (- \frac{3}{4 e ^{2}} + \frac{1}{4})

+1

Dezimale

1.33648 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{9 x}{e ^{2 x}} d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{1} \frac{x}{e ^{2 x}} d x

Wende die partielle Integration an

= 9 [- \frac{1}{2} e^{- 2 x} x - \int - \frac{1}{2} e^{- 2 x} d x]_{0}^{1}

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

= 9 [- \frac{1}{2} e^{- 2 x} x - \frac{1}{4} e^{- 2 x}]_{0}^{1}

Berechne die Grenzen:

- \frac{3}{4 e ^{2}} + \frac{1}{4}

= 9 (- \frac{3}{4 e ^{2}} + \frac{1}{4})

Graph

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