integral from-3 to 3 of |x^2-1|

Lösung

\int_{- 3}^{3} x^{2} - 1 d x

\frac{44}{3}

Dezimale

14.66666 \dots

Schritte zur Lösung

\int_{- 3}^{3} x^{2} - 1 d x

Entferne die Extremwerte

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

\int_{- 3}^{- 1} x^{2} - 1 d x = \frac{20}{3}

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

\int_{1}^{3} x^{2} - 1 d x = \frac{20}{3}

= \frac{20}{3} + \frac{4}{3} + \frac{20}{3}

Vereinfache

\frac{20}{3} + \frac{4}{3} + \frac{20}{3} : \frac{44}{3}

= \frac{44}{3}

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