integral from-2 to 4 of |x^2-2x-3|

Lösung

\int_{- 2}^{4} x^{2} - 2 x - 3 d x

\frac{46}{3}

Dezimale

15.33333 \dots

Schritte zur Lösung

\int_{- 2}^{4} x^{2} - 2 x - 3 d x

Entferne die Extremwerte

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

\int_{- 2}^{- 1} x^{2} - 2 x - 3 d x = \frac{7}{3}

\int_{- 1}^{3} - x^{2} + 2 x + 3 d x = \frac{32}{3}

\int_{3}^{4} x^{2} - 2 x - 3 d x = \frac{7}{3}

= \frac{7}{3} + \frac{32}{3} + \frac{7}{3}

Vereinfache

\frac{7}{3} + \frac{32}{3} + \frac{7}{3} : \frac{46}{3}

= \frac{46}{3}

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