integral from 3 to-3 of 9-x^2

Lösung

\int_{3}^{- 3} 9 - x^{2} d x

- 36

Schritte zur Lösung

\int_{3}^{- 3} 9 - x^{2} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 3}^{3} 9 - 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} 9 d x - \int_{- 3}^{3} x^{2} d x)

\int_{- 3}^{3} 9 d x = 54

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

= - (54 - 18)

Vereinfache

= - 36

\int_{- 3}^{- 1} \frac{1}{x ^{2}} d x

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