integral from 0 to 2 of 300e^{(3x-4)}

Lösung

\int_{0}^{2} 300 e^{(3 x - 4)} d x

100 (e^{2} - \frac{1}{e ^{4}})

Dezimale

737.07404 \dots

Schritte zur Lösung

\int_{0}^{2} 300 e^{3 x - 4} d x

Entferne die Konstante:

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

= 300 \cdot \int_{0}^{2} e^{3 x - 4} d x

Wende U-Substitution an

= 300 \cdot \int_{- 4}^{2} e^{u} \frac{1}{3} d u

Entferne die Konstante:

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

= 300 \cdot \frac{1}{3} \cdot \int_{- 4}^{2} e^{u} d u

Nutze das gemeinsame Integral :

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

= 300 \cdot \frac{1}{3} [e^{u}]_{- 4}^{2}

Vereinfache

300 \cdot \frac{1}{3} [e^{u}]_{- 4}^{2} : 100 [e^{u}]_{- 4}^{2}

= 100 [e^{u}]_{- 4}^{2}

Berechne die Grenzen:

e^{2} - \frac{1}{e ^{4}}

= 100 (e^{2} - \frac{1}{e ^{4}})

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