integral from 0 to 1 of (8y)/(e^{2y)}

Lösung

\int_{0}^{1} \frac{8 y}{e ^{2 y}} d y

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

Dezimale

1.18798 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{8 y}{e ^{2 y}} d y

Entferne die Konstante:

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

= 8 \cdot \int_{0}^{1} \frac{y}{e ^{2 y}} d y

Wende die partielle Integration an

= 8 [- \frac{1}{2} e^{- 2 y} y - \int - \frac{1}{2} e^{- 2 y} d y]_{0}^{1}

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

= 8 [- \frac{1}{2} e^{- 2 y} y - \frac{1}{4} e^{- 2 y}]_{0}^{1}

Berechne die Grenzen:

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

= 8 (- \frac{3}{4 e ^{2}} + \frac{1}{4})

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