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

Lösung

\int_{- 1}^{0} ∣ x ∣ - 1 d x

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

\int_{- 1}^{0} ∣ x ∣ - 1 d x

Entferne die Extremwerte

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

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

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

= - (- \frac{1}{2}) - 1

Vereinfache

- (- \frac{1}{2}) - 1 : - \frac{1}{2}

= - \frac{1}{2}

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