integral from 0 to 2 of 9e^{3x}

Lösung

\int_{0}^{2} 9 e^{3 x} d x

3 (e^{6} - 1)

Dezimale

1207.28638 \dots

Schritte zur Lösung

\int_{0}^{2} 9 e^{3 x} d x

Entferne die Konstante:

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

= 9 \cdot \int_{0}^{2} e^{3 x} d x

Wende U-Substitution an

= 9 \cdot \int_{0}^{6} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 9 \cdot \frac{1}{3} \cdot \int_{0}^{6} e^{u} d u

Nutze das gemeinsame Integral :

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

= 9 \cdot \frac{1}{3} [e^{u}]_{0}^{6}

Vereinfache

9 \cdot \frac{1}{3} [e^{u}]_{0}^{6} : 3 [e^{u}]_{0}^{6}

= 3 [e^{u}]_{0}^{6}

Berechne die Grenzen:

e^{6} - 1

= 3 (e^{6} - 1)

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