integral from-5 to 5 of (8-|x|)

Lösung

\int_{- 5}^{5} (8 - ∣ x ∣) d x

55

Schritte zur Lösung

\int_{- 5}^{5} 8 - ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- 5}^{0} 8 - (- x) d x + \int_{0}^{5} 8 - x d x

\int_{- 5}^{0} 8 - (- x) d x = \frac{55}{2}

\int_{0}^{5} 8 - x d x = \frac{55}{2}

= \frac{55}{2} + \frac{55}{2}

Vereinfache

\frac{55}{2} + \frac{55}{2} : 55

= 55

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