integral from-3 to 3 of [(18-x^2)-(x^2)]

Lösung

\int_{- 3}^{3} [(18 - x^{2}) - (x^{2})] d x

72

Schritte zur Lösung

\int_{- 3}^{3} 18 - x^{2} - x^{2} d x

Vereinfache

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

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

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

= 108 - 36

Vereinfache

= 72

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