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Beliebt Rechnen >

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

Lösung

\int_{- 1}^{1} π (1 - x^{2})^{2} d x

Lösung

π \frac{16}{15}

+1

Dezimale

3.35103 \dots

Schritte zur Lösung

\int_{- 1}^{1} π (1 - x^{2})^{2} d x

Entferne die Konstante:

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

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

Multipliziere aus

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

= π \cdot \int_{- 1}^{1} 1 - 2 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

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

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

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

\int_{- 1}^{1} x^{4} d x = \frac{2}{5}

= π (2 - \frac{4}{3} + \frac{2}{5})

Füge

2 - \frac{4}{3} + \frac{2}{5}

zusammen:

\frac{16}{15}

= π \frac{16}{15}

Graph

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