integral from 0 to 2 of 3x(x-5)

Lösung

\int_{0}^{2} 3 x (x - 5) d x

- 22

Schritte zur Lösung

\int_{0}^{2} 3 x (x - 5) d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{2} x (x - 5) d x

Multipliziere aus

x (x - 5) : x^{2} - 5 x

= 3 \cdot \int_{0}^{2} x^{2} - 5 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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 5 x d x = 10

= 3 (\frac{8}{3} - 10)

Vereinfache

3 (\frac{8}{3} - 10) : - 22

= - 22

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