integral from-1 to 1 of (8-|x|)

Lösung

\int_{- 1}^{1} (8 - ∣ x ∣) d x

15

Schritte zur Lösung

\int_{- 1}^{1} 8 - ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- 1}^{0} 8 - (- x) d x + \int_{0}^{1} 8 - x d x

\int_{- 1}^{0} 8 - (- x) d x = \frac{15}{2}

\int_{0}^{1} 8 - x d x = \frac{15}{2}

= \frac{15}{2} + \frac{15}{2}

Vereinfache

\frac{15}{2} + \frac{15}{2} : 15

= 15

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