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Beliebt Rechnen >

integral from 0 to 1 of (6x-9x^2)5x

Lösung

\int_{0}^{1} (6 x - 9 x^{2}) 5 x d x

Lösung

- \frac{5}{4}

+1

Dezimale

- 1.25

Schritte zur Lösung

\int_{0}^{1} (6 x - 9 x^{2}) \cdot 5 x d x

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{1} (6 x - 9 x^{2}) x d x

Multipliziere aus

(6 x - 9 x^{2}) x : 6 x^{2} - 9 x^{3}

= 5 \cdot \int_{0}^{1} 6 x^{2} - 9 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

= 5 (\int_{0}^{1} 6 x^{2} d x - \int_{0}^{1} 9 x^{3} d x)

\int_{0}^{1} 6 x^{2} d x = 2

\int_{0}^{1} 9 x^{3} d x = \frac{9}{4}

= 5 (2 - \frac{9}{4})

Vereinfache

5 (2 - \frac{9}{4}) : - \frac{5}{4}

= - \frac{5}{4}

Graph

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