integral from 0 to ln(3) of (e^{x+y})

Lösung

\int_{0}^{l n (3)} (e^{x + y}) d y

e^{x} \cdot 2

Schritte zur Lösung

\int_{0}^{l n (3)} e^{x + y} d y

e^{x + y} = e^{x} e^{y}

= \int_{0}^{l n (3)} e^{x} e^{y} d y

Entferne die Konstante:

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

= e^{x} \cdot \int_{0}^{l n (3)} e^{y} d y

Nutze das gemeinsame Integral :

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

= e^{x} [e^{y}]_{0}^{l n (3)}

Berechne die Grenzen:

2

= e^{x} \cdot 2

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