integral from-3 to 3 of (e^{x+3})

Lösung

\int_{- 3}^{3} (e^{x + 3}) d x

e^{6} - 1

Dezimale

402.42879 \dots

Schritte zur Lösung

\int_{- 3}^{3} e^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

= \int_{- 3}^{3} e^{3} e^{x} d x

Entferne die Konstante:

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

= e^{3} \cdot \int_{- 3}^{3} e^{x} d x

Nutze das gemeinsame Integral :

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

= e^{3} [e^{x}]_{- 3}^{3}

Berechne die Grenzen:

e^{3} - \frac{1}{e ^{3}}

= e^{3} (e^{3} - \frac{1}{e ^{3}})

Vereinfache

= e^{6} - 1

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