integral from 3 to 6 of 10000e^{0.02x}

Lösung

\int_{3}^{6} 10000 e^{0.02 x} d x

32830.15251 \dots

Schritte zur Lösung

\int_{3}^{6} 10000 e^{0.02 x} d x

Entferne die Konstante:

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

= 10000 \cdot \int_{3}^{6} e^{0.02 x} d x

Wende U-Substitution an

= 10000 \cdot \int_{0.06}^{0.12} e^{u} \frac{1}{0.02} d u

Entferne die Konstante:

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

= 10000 \cdot \frac{1}{0.02} \cdot \int_{0.06}^{0.12} e^{u} d u

Vereinfache

= 10000 \cdot 50 \cdot \int_{0.06}^{0.12} e^{u} d u

Nutze das gemeinsame Integral :

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

= 10000 \cdot 50 [e^{u}]_{0.06}^{0.12}

Vereinfache

= 500000 [e^{u}]_{0.06}^{0.12}

Berechne die Grenzen:

0.06566 \dots

= 500000 \cdot 0.06566 \dots

Vereinfache

= 32830.15251 \dots

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