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Beliebt Rechnen >

integral from-1 to 1 of (2sqrt(1-x^2))^2

Lösung

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

Lösung

\frac{16}{3}

+1

Dezimale

5.33333 \dots

Schritte zur Lösung

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

Vereinfache

(2 1 - x^{2})^{2} : 4 (1 - x^{2})

= \int_{- 1}^{1} 4 (1 - x^{2}) d x

Entferne die Konstante:

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

= 4 \cdot \int_{- 1}^{1} 1 - 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

= 4 (\int_{- 1}^{1} 1 d x - \int_{- 1}^{1} x^{2} d x)

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

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

= 4 (2 - \frac{2}{3})

Vereinfache

4 (2 - \frac{2}{3}) : \frac{16}{3}

= \frac{16}{3}

Graph

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