integral from 0 to 3 of 10e^{2x}

Lösung

\int_{0}^{3} 10 e^{2 x} d x

5 (e^{6} - 1)

Dezimale

2012.14396 \dots

Schritte zur Lösung

\int_{0}^{3} 10 e^{2 x} d x

Entferne die Konstante:

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

= 10 \cdot \int_{0}^{3} e^{2 x} d x

Wende U-Substitution an

= 10 \cdot \int_{0}^{6} e^{u} \frac{1}{2} d u

Entferne die Konstante:

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

= 10 \cdot \frac{1}{2} \cdot \int_{0}^{6} e^{u} d u

Nutze das gemeinsame Integral :

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

= 10 \cdot \frac{1}{2} [e^{u}]_{0}^{6}

Vereinfache

10 \cdot \frac{1}{2} [e^{u}]_{0}^{6} : 5 [e^{u}]_{0}^{6}

= 5 [e^{u}]_{0}^{6}

Berechne die Grenzen:

e^{6} - 1

= 5 (e^{6} - 1)

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