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Beliebt Rechnen >

integral from 0 to 1 of 2/3 x^2(x+1)

Lösung

\int_{0}^{1} \frac{2}{3} x^{2} (x + 1) d x

Lösung

\frac{7}{18}

+1

Dezimale

0.38888 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{2}{3} x^{2} (x + 1) d x

Entferne die Konstante:

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

= \frac{2}{3} \cdot \int_{0}^{1} x^{2} (x + 1) d x

Multipliziere aus

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

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

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

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

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

= \frac{2}{3} (\frac{1}{4} + \frac{1}{3})

Vereinfache

\frac{2}{3} (\frac{1}{4} + \frac{1}{3}) : \frac{7}{18}

= \frac{7}{18}

Graph

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