integral from-4 to 4 of |x^2+x-2|

Lösung

\int_{- 4}^{4} x^{2} + x - 2 d x

\frac{107}{3}

Dezimale

35.66666 \dots

Schritte zur Lösung

\int_{- 4}^{4} x^{2} + x - 2 d x

Entferne die Extremwerte

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

\int_{- 4}^{- 2} x^{2} + x - 2 d x = \frac{26}{3}

\int_{- 2}^{1} - x^{2} - x + 2 d x = \frac{9}{2}

\int_{1}^{4} x^{2} + x - 2 d x = \frac{45}{2}

= \frac{26}{3} + \frac{9}{2} + \frac{45}{2}

Vereinfache

\frac{26}{3} + \frac{9}{2} + \frac{45}{2} : \frac{107}{3}

= \frac{107}{3}

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