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Beliebt Rechnen >

integral from 2 to 4 of x((2x-3))/6

Lösung

\int_{2}^{4} x \frac{( 2 x - 3 )}{6} d x

Lösung

\frac{29}{9}

+1

Dezimale

3.22222 \dots

Schritte zur Lösung

\int_{2}^{4} x \frac{2 x - 3}{6} d x

Entferne die Konstante:

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

= \frac{1}{6} \cdot \int_{2}^{4} x (2 x - 3) d x

Multipliziere aus

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

= \frac{1}{6} \cdot \int_{2}^{4} 2 x^{2} - 3 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{1}{6} (\int_{2}^{4} 2 x^{2} d x - \int_{2}^{4} 3 x d x)

\int_{2}^{4} 2 x^{2} d x = \frac{112}{3}

\int_{2}^{4} 3 x d x = 18

= \frac{1}{6} (\frac{112}{3} - 18)

Vereinfache

\frac{1}{6} (\frac{112}{3} - 18) : \frac{29}{9}

= \frac{29}{9}

Graph

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