integral from-3 to 4 of e^{x+7}

Lösung

\int_{- 3}^{4} e^{x + 7} d x

e^{11} - e^{4}

Dezimale

59819.54356 \dots

Schritte zur Lösung

\int_{- 3}^{4} e^{x + 7} d x

e^{x + 7} = e^{7} e^{x}

= \int_{- 3}^{4} e^{7} e^{x} d x

Entferne die Konstante:

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

= e^{7} \cdot \int_{- 3}^{4} e^{x} d x

Nutze das gemeinsame Integral :

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

= e^{7} [e^{x}]_{- 3}^{4}

Berechne die Grenzen:

e^{4} - \frac{1}{e ^{3}}

= e^{7} (e^{4} - \frac{1}{e ^{3}})

Vereinfache

= e^{11} - e^{4}

\int_{- 2}^{2} x^{3} - 3 x + 0.5 d x

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