integral from 0 to 1 of (1-x)x

Lösung

\int_{0}^{1} (1 - x) x d x

\frac{1}{6}

Dezimale

0.16666 \dots

Schritte zur Lösung

\int_{0}^{1} (1 - x) x d x

Multipliziere aus

(1 - x) x : x - x^{2}

= \int_{0}^{1} x - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x d x - \int_{0}^{1} x^{2} d x

\int_{0}^{1} x d x = \frac{1}{2}

\int_{0}^{1} x^{2} d x = \frac{1}{3}

= \frac{1}{2} - \frac{1}{3}

Vereinfache

\frac{1}{2} - \frac{1}{3} : \frac{1}{6}

= \frac{1}{6}

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