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Beliebt Rechnen >

integral from 0 to 1 of x(2(x+2))/5

Lösung

\int_{0}^{1} x \frac{2 ( x + 2 )}{5} d x

Lösung

\frac{8}{15}

+1

Dezimale

0.53333 \dots

Schritte zur Lösung

\int_{0}^{1} x \frac{2 ( x + 2 )}{5} d x

Entferne die Konstante:

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

= \frac{2}{5} \cdot \int_{0}^{1} x (x + 2) d x

Multipliziere aus

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

= \frac{2}{5} \cdot \int_{0}^{1} x^{2} + 2 x 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}{5} (\int_{0}^{1} x^{2} d x + \int_{0}^{1} 2 x d x)

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

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

= \frac{2}{5} (\frac{1}{3} + 1)

Vereinfache

\frac{2}{5} (\frac{1}{3} + 1) : \frac{8}{15}

= \frac{8}{15}

Graph

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