integral from 0 to 2 of 2e^{2z}

Lösung

\int_{0}^{2} 2 e^{2 z} d z

e^{4} - 1

Dezimale

53.59815 \dots

Schritte zur Lösung

\int_{0}^{2} 2 e^{2 z} d z

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} e^{2 z} d z

Wende U-Substitution an

= 2 \cdot \int_{0}^{4} e^{u} \frac{1}{2} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{0}^{4} e^{u} d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{2} [e^{u}]_{0}^{4}

Vereinfache

2 \cdot \frac{1}{2} [e^{u}]_{0}^{4} : [e^{u}]_{0}^{4}

= [e^{u}]_{0}^{4}

Berechne die Grenzen:

e^{4} - 1

= e^{4} - 1

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