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

Lösung

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

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

Dezimale

0.14849 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [- \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}

= [- \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}

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