integral from-1 to 2 of |x-x^2|

Lösung

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

\frac{11}{6}

Dezimale

1.83333 \dots

Schritte zur Lösung

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

Entferne die Extremwerte

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

\int_{- 1}^{0} - x + x^{2} d x = \frac{5}{6}

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

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

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

Vereinfache

\frac{5}{6} + \frac{1}{6} + \frac{5}{6} : \frac{11}{6}

= \frac{11}{6}

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