integral from 0 to 3 of 450.268e^{1.12567t}

Lösung

\int_{0}^{3} 450.268 e^{1.12567 t} d t

11313.23346 \dots

Schritte zur Lösung

\int_{0}^{3} 450.268 e^{1.12567 t} d t

Entferne die Konstante:

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

= 450.268 \cdot \int_{0}^{3} e^{1.12567 t} d t

Wende U-Substitution an

= 450.268 \cdot \int_{0}^{3.37701} e^{u} \frac{1}{1.12567} d u

Entferne die Konstante:

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

= 450.268 \cdot \frac{1}{1.12567} \cdot \int_{0}^{3.37701} e^{u} d u

Vereinfache

= 450.268 \cdot 0.88835 \dots \cdot \int_{0}^{3.37701} e^{u} d u

Nutze das gemeinsame Integral :

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

= 450.268 \cdot 0.88835 \dots [e^{u}]_{0}^{3.37701}

Vereinfache

= 400 [e^{u}]_{0}^{3.37701}

Berechne die Grenzen:

28.28308 \dots

= 400 \cdot 28.28308 \dots

Vereinfache

= 11313.23346 \dots

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