integral from 0 to 10 of |x-7|

Lösung

\int_{0}^{10} ∣ x - 7 ∣ d x

29

Schritte zur Lösung

\int_{0}^{10} ∣ x - 7 ∣ d x

Entferne die Extremwerte

= \int_{0}^{7} - x + 7 d x + \int_{7}^{10} x - 7 d x

\int_{0}^{7} - x + 7 d x = \frac{49}{2}

\int_{7}^{10} x - 7 d x = \frac{9}{2}

= \frac{49}{2} + \frac{9}{2}

Vereinfache

\frac{49}{2} + \frac{9}{2} : 29

= 29

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