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Beliebt Rechnen >

integral from-2 to 4 of (1+2x-3x^2+x^3)

Lösung

\int_{- 2}^{4} (1 + 2 x - 3 x^{2} + x^{3}) d x

Lösung

6

Schritte zur Lösung

\int_{- 2}^{4} 1 + 2 x - 3 x^{2} + 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_{- 2}^{4} 1 d x + \int_{- 2}^{4} 2 x d x - \int_{- 2}^{4} 3 x^{2} d x + \int_{- 2}^{4} x^{3} d x

\int_{- 2}^{4} 1 d x = 6

\int_{- 2}^{4} 2 x d x = 12

\int_{- 2}^{4} 3 x^{2} d x = 72

\int_{- 2}^{4} x^{3} d x = 60

= 6 + 12 - 72 + 60

Vereinfache

= 6

Graph

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