integral from-1 to 1 of x(1-|x|)

Lösung

\int_{- 1}^{1} x (1 - ∣ x ∣) d x

0

Schritte zur Lösung

\int_{- 1}^{1} x (1 - ∣ x ∣) d x

Entferne die Extremwerte

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

\int_{- 1}^{0} x (1 - (- x)) d x = - \frac{1}{6}

\int_{0}^{1} x (1 - x) d x = \frac{1}{6}

= - \frac{1}{6} + \frac{1}{6}

Vereinfache

= 0

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