integral from 0 to 2 of 1-c|1-x|

Lösung

\int_{0}^{2} 1 - c ∣ 1 - x ∣ d x

- c + 2

Schritte zur Lösung

\int_{0}^{2} 1 - c ∣ 1 - x ∣ d x

Entferne die Extremwerte

= \int_{0}^{1} 1 - c (1 - x) d x + \int_{1}^{2} 1 - c (- 1 + x) d x

\int_{0}^{1} 1 - c (1 - x) d x = 1 - \frac{1}{2} c

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

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

Vereinfache

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

= - c + 2

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