integral from 0 to 2 of |x^2-x|

Lösung

\int_{0}^{2} x^{2} - x d x

1

Schritte zur Lösung

\int_{0}^{2} x^{2} - x d x

Entferne die Extremwerte

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

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

\int_{1}^{2} x^{2} - x d x = \frac{5}{6}

= \frac{1}{6} + \frac{5}{6}

Vereinfache

\frac{1}{6} + \frac{5}{6} : 1

= 1

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