integral from-2 to 5 of |6x-x^2|

Lösung

\int_{- 2}^{5} 6 x - x^{2} d x

48

Schritte zur Lösung

\int_{- 2}^{5} 6 x - x^{2} d x

Entferne die Extremwerte

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

\int_{- 2}^{0} - 6 x + x^{2} d x = \frac{44}{3}

\int_{0}^{5} 6 x - x^{2} d x = \frac{100}{3}

= \frac{44}{3} + \frac{100}{3}

Vereinfache

\frac{44}{3} + \frac{100}{3} : 48

= 48

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