integral from 0 to 2 of |t-1|

Lösung

\int_{0}^{2} ∣ t - 1 ∣ d t

1

Schritte zur Lösung

\int_{0}^{2} ∣ t - 1 ∣ d t

Entferne die Extremwerte

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

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

\int_{1}^{2} t - 1 d t = \frac{1}{2}

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

Vereinfache

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

= 1

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