integral from-1 to 1 of e^{-|x|}

Lösung

\int_{- 1}^{1} e^{- ∣ x ∣} d x

- \frac{2}{e} + 2

Dezimale

1.26424 \dots

Schritte zur Lösung

\int_{- 1}^{1} e^{- ∣ x ∣} d x

Entferne die Extremwerte

= \int_{- 1}^{0} e^{- (- x)} d x + \int_{0}^{1} e^{- x} d x

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

\int_{0}^{1} e^{- x} d x = 1 - \frac{1}{e}

= 1 - \frac{1}{e} + 1 - \frac{1}{e}

Vereinfache

1 - \frac{1}{e} + 1 - \frac{1}{e} : - \frac{2}{e} + 2

= - \frac{2}{e} + 2

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