integral from 0 to 1 of (x^2-1)^2

Lösung

\int_{0}^{1} (x^{2} - 1)^{2} d x

\frac{8}{15}

Dezimale

0.53333 \dots

Schritte zur Lösung

\int_{0}^{1} (x^{2} - 1)^{2} d x

Multipliziere aus

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

= \int_{0}^{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_{0}^{1} x^{4} d x - \int_{0}^{1} 2 x^{2} d x + \int_{0}^{1} 1 d x

\int_{0}^{1} x^{4} d x = \frac{1}{5}

\int_{0}^{1} 2 x^{2} d x = \frac{2}{3}

\int_{0}^{1} 1 d x = 1

= \frac{1}{5} - \frac{2}{3} + 1

Vereinfache

\frac{1}{5} - \frac{2}{3} + 1 : \frac{8}{15}

= \frac{8}{15}

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