integral from 0 to 6 of x(6-x)

Lösung

\int_{0}^{6} x (6 - x) d x

36

Schritte zur Lösung

\int_{0}^{6} x (6 - x) d x

Multipliziere aus

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

= \int_{0}^{6} 6 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

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

\int_{0}^{6} 6 x d x = 108

\int_{0}^{6} x^{2} d x = 72

= 108 - 72

Vereinfache

= 36

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