integral from 0 to 5 of 300e^{0.2x-1}

Lösung

\int_{0}^{5} 300 e^{0.2 x - 1} d x

1500 (1 - \frac{1}{e})

Dezimale

948.18083 \dots

Schritte zur Lösung

\int_{0}^{5} 300 e^{0.2 x - 1} d x

Entferne die Konstante:

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

= 300 \cdot \int_{0}^{5} e^{0.2 x - 1} d x

Wende U-Substitution an

= 300 \cdot \int_{- 1}^{0} e^{u} \frac{1}{0.2} d u

Entferne die Konstante:

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

= 300 \cdot \frac{1}{0.2} \cdot \int_{- 1}^{0} e^{u} d u

Vereinfache

= 300 \cdot 5 \cdot \int_{- 1}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= 300 \cdot 5 [e^{u}]_{- 1}^{0}

Vereinfache

= 1500 [e^{u}]_{- 1}^{0}

Berechne die Grenzen:

1 - \frac{1}{e}

= 1500 (1 - \frac{1}{e})

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