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

Lösung

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

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

Dezimale

- 0.21572 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Addiere gleiche Elemente:

- \frac{1}{2} e^{2 x} - \frac{1}{2} e^{2 x} = - e^{2 x}

= [e^{2 x} x - e^{2 x}]_{- 2}^{- 1}

Berechne die Grenzen:

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

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

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