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

Lösung

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

4

Schritte zur Lösung

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

Multipliziere aus

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

= 3 \cdot \int_{0}^{2} 2 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

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

\int_{0}^{2} 2 x d x = 4

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

= 3 (4 - \frac{8}{3})

Vereinfache

3 (4 - \frac{8}{3}) : 4

= 4

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