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

Lösung

\int_{- 2}^{1} ∣ x - 1 ∣ d x

\frac{9}{2}

Dezimale

4.5

Schritte zur Lösung

\int_{- 2}^{1} ∣ x - 1 ∣ d x

Entferne die Extremwerte

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

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

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

= - (- \frac{3}{2}) + 3

Vereinfache

- (- \frac{3}{2}) + 3 : \frac{9}{2}

= \frac{9}{2}

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