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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{16}{15}

+1

Dezimale

1.06666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{- 1}^{1} x^{4} - 2 x^{2} + 1 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_{- 1}^{1} x^{4} d x - \int_{- 1}^{1} 2 x^{2} d x + \int_{- 1}^{1} 1 d x

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

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

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

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

Vereinfache

\frac{2}{5} - \frac{4}{3} + 2 : \frac{16}{15}

= \frac{16}{15}

Graph

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