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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1296}{5}

+1

Dezimale

259.2

Schritte zur Lösung

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

Multipliziere aus

(9 - x^{2})^{2} : 81 - 18 x^{2} + x^{4}

= \int_{- 3}^{3} 81 - 18 x^{2} + x^{4} 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} 81 d x - \int_{- 3}^{3} 18 x^{2} d x + \int_{- 3}^{3} x^{4} d x

\int_{- 3}^{3} 81 d x = 486

\int_{- 3}^{3} 18 x^{2} d x = 324

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

= 486 - 324 + \frac{486}{5}

Vereinfache

486 - 324 + \frac{486}{5} : \frac{1296}{5}

= \frac{1296}{5}

Graph

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