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

Lösung

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

- \frac{5}{4 e ^{4}} + \frac{1}{4}

Dezimale

0.22710 \dots

Schritte zur Lösung

\int_{0}^{2} \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}^{2}

\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}^{2}

Berechne die Grenzen:

- \frac{5}{4 e ^{4}} + \frac{1}{4}

= - \frac{5}{4 e ^{4}} + \frac{1}{4}

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