integral from 0 to 1 of xax^{a-1}

Lösung

\int_{0}^{1} x a x^{a - 1} d x

\frac{a}{a + 1}

Schritte zur Lösung

\int_{0}^{1} x a x^{a - 1} d x

Entferne die Konstante:

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

= a \cdot \int_{0}^{1} x x^{a - 1} d x

Vereinfache

x x^{a - 1} : x^{a}

= a \cdot \int_{0}^{1} x^{a} d x

Wende die Potenzregel an

= a [\frac{x ^{a + 1}}{a + 1}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{a + 1}

= a \frac{1}{a + 1}

Vereinfache

= \frac{a}{a + 1}

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