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

Lösung

\int_{- 1}^{1} ∣ x - 2 ∣ d x

4

Schritte zur Lösung

\int_{- 1}^{1} ∣ x - 2 ∣ d x

Entferne die Extremwerte

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= - 0 + 4

Vereinfache

= 4

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