integral from 0 to 2 of 9000e^{0.06t}

Lösung

\int_{0}^{2} 9000 e^{0.06 t} d t

19124.52773 \dots

Schritte zur Lösung

\int_{0}^{2} 9000 e^{0.06 t} d t

Entferne die Konstante:

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

= 9000 \cdot \int_{0}^{2} e^{0.06 t} d t

Wende U-Substitution an

= 9000 \cdot \int_{0}^{0.12} e^{u} \frac{1}{0.06} d u

Entferne die Konstante:

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

= 9000 \cdot \frac{1}{0.06} \cdot \int_{0}^{0.12} e^{u} d u

Vereinfache

= 9000 \cdot 16.66666 \dots \cdot \int_{0}^{0.12} e^{u} d u

Nutze das gemeinsame Integral :

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

= 9000 \cdot 16.66666 \dots [e^{u}]_{0}^{0.12}

Vereinfache

= 150000 [e^{u}]_{0}^{0.12}

Berechne die Grenzen:

0.12749 \dots

= 150000 \cdot 0.12749 \dots

Vereinfache

= 19124.52773 \dots

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