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

Lösung

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

- e^{2} + 2 e + \frac{- 2 e ^{3} + e ^{8} - 2 e ^{6} + 1}{2 e ^{5}}

Dezimale

5.24002 \dots

Schritte zur Lösung

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

Entferne die Extremwerte

= \int_{- 2}^{1} - e^{2 x - 1} + e^{x} d x + \int_{1}^{2} e^{2 x - 1} - e^{x} d x

\int_{- 2}^{1} - e^{2 x - 1} + e^{x} d x = - \frac{e ^{6} - 1}{2 e ^{5}} + e - \frac{1}{e ^{2}}

\int_{1}^{2} e^{2 x - 1} - e^{x} d x = \frac{e ^{3} - e}{2} - e^{2} + e

= - \frac{e ^{6} - 1}{2 e ^{5}} + e - \frac{1}{e ^{2}} + \frac{e ^{3} - e}{2} - e^{2} + e

Vereinfache

- \frac{e ^{6} - 1}{2 e ^{5}} + e - \frac{1}{e ^{2}} + \frac{e ^{3} - e}{2} - e^{2} + e : - e^{2} + 2 e + \frac{- 2 e ^{3} + e ^{8} - 2 e ^{6} + 1}{2 e ^{5}}

= - e^{2} + 2 e + \frac{- 2 e ^{3} + e ^{8} - 2 e ^{6} + 1}{2 e ^{5}}

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