integral from 2 to 4 of 4e^{5x-8}

Lösung

\int_{2}^{4} 4 e^{5 x - 8} d x

\frac{4 ( e ^{12} - e ^{2} )}{5}

Dezimale

130197.92189 \dots

Schritte zur Lösung

\int_{2}^{4} 4 e^{5 x - 8} d x

Entferne die Konstante:

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

= 4 \cdot \int_{2}^{4} e^{5 x - 8} d x

Wende U-Substitution an

= 4 \cdot \int_{2}^{12} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{5} \cdot \int_{2}^{12} e^{u} d u

Nutze das gemeinsame Integral :

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

= 4 \cdot \frac{1}{5} [e^{u}]_{2}^{12}

Vereinfache

4 \cdot \frac{1}{5} [e^{u}]_{2}^{12} : \frac{4}{5} [e^{u}]_{2}^{12}

= \frac{4}{5} [e^{u}]_{2}^{12}

Berechne die Grenzen:

e^{12} - e^{2}

= \frac{4}{5} (e^{12} - e^{2})

Vereinfache

= \frac{4 ( e ^{12} - e ^{2} )}{5}

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