integral from 0 to 2 of x(4-x^2)

Lösung

\int_{0}^{2} x (4 - x^{2}) d x

4

Schritte zur Lösung

\int_{0}^{2} x (4 - x^{2}) d x

Multipliziere aus

x (4 - x^{2}) : 4 x - x^{3}

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

= \int_{0}^{2} 4 x d x - \int_{0}^{2} x^{3} d x

\int_{0}^{2} 4 x d x = 8

\int_{0}^{2} x^{3} d x = 4

= 8 - 4

Vereinfache

= 4

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