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Beliebt Rechnen >

integral from 0 to 1 of (1-x^3)^2

Lösung

\int_{0}^{1} (1 - x^{3})^{2} d x

Lösung

\frac{9}{14}

+1

Dezimale

0.64285 \dots

Schritte zur Lösung

\int_{0}^{1} (1 - x^{3})^{2} d x

Multipliziere aus

(1 - x^{3})^{2} : 1 - 2 x^{3} + x^{6}

= \int_{0}^{1} 1 - 2 x^{3} + x^{6} 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} 1 d x - \int_{0}^{1} 2 x^{3} d x + \int_{0}^{1} x^{6} d x

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

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

\int_{0}^{1} x^{6} d x = \frac{1}{7}

= 1 - \frac{1}{2} + \frac{1}{7}

Vereinfache

1 - \frac{1}{2} + \frac{1}{7} : \frac{9}{14}

= \frac{9}{14}

Graph

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