integral from 0 to 6 of |x-5|

Lösung

\int_{0}^{6} ∣ x - 5 ∣ d x

13

Schritte zur Lösung

\int_{0}^{6} ∣ x - 5 ∣ d x

Entferne die Extremwerte

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

\int_{0}^{5} - x + 5 d x = \frac{25}{2}

\int_{5}^{6} x - 5 d x = \frac{1}{2}

= \frac{25}{2} + \frac{1}{2}

Vereinfache

\frac{25}{2} + \frac{1}{2} : 13

= 13

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