integral from 0 to 1 of ye^{xy}

Lösung

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

e^{y} - 1

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

= y \cdot \int_{0}^{y} \frac{e ^{u}}{y} d u

Entferne die Konstante:

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

= y \frac{1}{y} \cdot \int_{0}^{y} e^{u} d u

Nutze das gemeinsame Integral :

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

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

Vereinfache

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

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

Berechne die Grenzen:

e^{y} - 1

= e^{y} - 1

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