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Beliebt Rechnen >

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

Lösung

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

Lösung

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

+1

Dezimale

0.49084 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{- 4}^{0} e^{u} \frac{1}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 4}^{0} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= \frac{1}{2} [e^{u}]_{- 4}^{0}

Berechne die Grenzen:

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

= \frac{1}{2} (1 - \frac{1}{e ^{4}})

Vereinfache

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

Graph

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