integral from 0 to 3 of |2x-x^2|

Lösung

\int_{0}^{3} 2 x - x^{2} d x

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

\int_{0}^{3} 2 x - x^{2} d x

Entferne die Extremwerte

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

\int_{0}^{2} 2 x - x^{2} d x = \frac{4}{3}

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

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

Vereinfache

\frac{4}{3} + \frac{4}{3} : \frac{8}{3}

= \frac{8}{3}

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