integral from 1 to 3 of |x-2|

Lösung

\int_{1}^{3} ∣ x - 2 ∣ d x

1

Schritte zur Lösung

\int_{1}^{3} ∣ x - 2 ∣ d x

Entferne die Extremwerte

= \int_{1}^{2} - x + 2 d x + \int_{2}^{3} x - 2 d x

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

\int_{2}^{3} x - 2 d x = \frac{1}{2}

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

Vereinfache

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

= 1

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