integral from 0 to 1 of x^9(1+x^{10})^9

Lösung

\int_{0}^{1} x^{9} (1 + x^{10})^{9} d x

\frac{1023}{100}

Dezimale

10.23

Schritte zur Lösung

\int_{0}^{1} x^{9} (1 + x^{10})^{9} d x

Wende U-Substitution an

= \int_{1}^{2} \frac{u ^{9}}{10} d u

Entferne die Konstante:

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

= \frac{1}{10} \cdot \int_{1}^{2} u^{9} d u

Wende die Potenzregel an

= \frac{1}{10} [\frac{u ^{10}}{10}]_{1}^{2}

Berechne die Grenzen:

\frac{1023}{10}

= \frac{1}{10} \cdot \frac{1023}{10}

Vereinfache

= \frac{1023}{100}

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