integral from 0 to 1 of 2e^{2x}

Lösung

\int_{0}^{1} 2 e^{2 x} d x

e^{2} - 1

Dezimale

6.38905 \dots

Schritte zur Lösung

\int_{0}^{1} 2 e^{2 x} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} e^{2 x} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

= [e^{u}]_{0}^{2}

Berechne die Grenzen:

e^{2} - 1

= e^{2} - 1

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