integral from 1 to 3 of 0.2e^{0.2t}

Lösung

\int_{1}^{3} 0.2 e^{0.2 t} d t

0.60071 \dots

Schritte zur Lösung

\int_{1}^{3} 0.2 e^{0.2 t} d t

Entferne die Konstante:

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

= 0.2 \cdot \int_{1}^{3} e^{0.2 t} d t

Wende U-Substitution an

= 0.2 \cdot \int_{0.2}^{0.6} e^{u} \frac{1}{0.2} d u

Entferne die Konstante:

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

= 0.2 \cdot \frac{1}{0.2} \cdot \int_{0.2}^{0.6} e^{u} d u

Vereinfache

= 0.2 \cdot 5 \cdot \int_{0.2}^{0.6} e^{u} d u

Nutze das gemeinsame Integral :

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

= 0.2 \cdot 5 [e^{u}]_{0.2}^{0.6}

Vereinfache

= [e^{u}]_{0.2}^{0.6}

Berechne die Grenzen:

0.60071 \dots

= 0.60071 \dots