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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{24}{5}

+1

Dezimale

4.8

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 1}^{1} (3 - 3 x^{2})^{2} d x

Multipliziere aus

(3 - 3 x^{2})^{2} : 9 - 18 x^{2} + 9 x^{4}

= \frac{1}{2} \cdot \int_{- 1}^{1} 9 - 18 x^{2} + 9 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

= \frac{1}{2} (\int_{- 1}^{1} 9 d x - \int_{- 1}^{1} 18 x^{2} d x + \int_{- 1}^{1} 9 x^{4} d x)

\int_{- 1}^{1} 9 d x = 18

\int_{- 1}^{1} 18 x^{2} d x = 12

\int_{- 1}^{1} 9 x^{4} d x = \frac{18}{5}

= \frac{1}{2} (18 - 12 + \frac{18}{5})

Vereinfache

\frac{1}{2} (18 - 12 + \frac{18}{5}) : \frac{24}{5}

= \frac{24}{5}

Graph

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