integral from 0 to 4 of |x-1|

Lösung

\int_{0}^{4} ∣ x - 1 ∣ d x

5

Schritte zur Lösung

\int_{0}^{4} ∣ x - 1 ∣ d x

Entferne die Extremwerte

= \int_{0}^{1} - x + 1 d x + \int_{1}^{4} x - 1 d x

\int_{0}^{1} - x + 1 d x = \frac{1}{2}

\int_{1}^{4} x - 1 d x = \frac{9}{2}

= \frac{1}{2} + \frac{9}{2}

Vereinfache

\frac{1}{2} + \frac{9}{2} : 5

= 5

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