integral from-1 to 1 of (5-|x|)

Lösung

\int_{- 1}^{1} (5 - ∣ x ∣) d x

9

Schritte zur Lösung

\int_{- 1}^{1} 5 - ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- 1}^{0} 5 - (- x) d x + \int_{0}^{1} 5 - x d x

\int_{- 1}^{0} 5 - (- x) d x = \frac{9}{2}

\int_{0}^{1} 5 - x d x = \frac{9}{2}

= \frac{9}{2} + \frac{9}{2}

Vereinfache

\frac{9}{2} + \frac{9}{2} : 9

= 9

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