integral from 0 to 3 of (3x(8-x))/(256)

Lösung

\int_{0}^{3} \frac{3 x ( 8 - x )}{256} d x

\frac{81}{256}

Dezimale

0.31640625

Schritte zur Lösung

\int_{0}^{3} \frac{3 x ( 8 - x )}{256} d x

Entferne die Konstante:

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

= \frac{3}{256} \cdot \int_{0}^{3} x (8 - x) d x

Multipliziere aus

x (8 - x) : 8 x - x^{2}

= \frac{3}{256} \cdot \int_{0}^{3} 8 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

= \frac{3}{256} (\int_{0}^{3} 8 x d x - \int_{0}^{3} x^{2} d x)

\int_{0}^{3} 8 x d x = 36

\int_{0}^{3} x^{2} d x = 9

= \frac{3}{256} (36 - 9)

Vereinfache

\frac{3}{256} (36 - 9) : \frac{81}{256}

= \frac{81}{256}

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