integral from 0 to 1 of x^2(1-x)

Lösung

\int_{0}^{1} x^{2} (1 - x) d x

\frac{1}{12}

Dezimale

0.08333 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} (1 - x) d x

Multipliziere aus

x^{2} (1 - x) : x^{2} - x^{3}

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

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

\int_{0}^{1} x^{3} d x = \frac{1}{4}

= \frac{1}{3} - \frac{1}{4}

Vereinfache

\frac{1}{3} - \frac{1}{4} : \frac{1}{12}

= \frac{1}{12}

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