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Beliebt Rechnen >

integral from 0 to 2 of (x-3)^2-(x-1)^2

Lösung

\int_{0}^{2} (x - 3)^{2} - (x - 1)^{2} d x

Lösung

8

Schritte zur Lösung

\int_{0}^{2} (x - 3)^{2} - (x - 1)^{2} d x

Vereinfache

(x - 3)^{2} - (x - 1)^{2} : - 4 x + 8

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

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

\int_{0}^{2} 8 d x = 16

= - 8 + 16

Vereinfache

= 8

Graph

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