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Beliebt Rechnen >

integral from-3 to 3 of (15-x^2)-(x^2-3)

Lösung

\int_{- 3}^{3} (15 - x^{2}) - (x^{2} - 3) d x

Lösung

72

Schritte zur Lösung

\int_{- 3}^{3} 15 - x^{2} - (x^{2} - 3) d x

Vereinfache

= \int_{- 3}^{3} - 2 x^{2} + 18 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_{- 3}^{3} 2 x^{2} d x + \int_{- 3}^{3} 18 d x

\int_{- 3}^{3} 2 x^{2} d x = 36

\int_{- 3}^{3} 18 d x = 108

= - 36 + 108

Vereinfache

= 72

Graph

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