integral from 0 to 4 of (x(x-1)(x-2))

Lösung

\int_{0}^{4} (x (x - 1) (x - 2)) d x

16

Schritte zur Lösung

\int_{0}^{4} x (x - 1) (x - 2) d x

Multipliziere aus

x (x - 1) (x - 2) : x^{3} - 3 x^{2} + 2 x

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

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

\int_{0}^{4} x^{3} d x = 64

\int_{0}^{4} 3 x^{2} d x = 64

\int_{0}^{4} 2 x d x = 16

= 64 - 64 + 16

Vereinfache

= 16

\int_{- \infty}^{- 6} x e^{x} d x

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