integral from-5 to 5 of 5|x|-x^2

Lösung

\int_{- 5}^{5} 5 ∣ x ∣ - x^{2} d x

\frac{125}{3}

Dezimale

41.66666 \dots

Schritte zur Lösung

\int_{- 5}^{5} 5 ∣ x ∣ - x^{2} d x

Entferne die Extremwerte

= \int_{- 5}^{0} 5 (- x) - x^{2} d x + \int_{0}^{5} 5 x - x^{2} d x

\int_{- 5}^{0} 5 (- x) - x^{2} d x = \frac{125}{6}

\int_{0}^{5} 5 x - x^{2} d x = \frac{125}{6}

= \frac{125}{6} + \frac{125}{6}

Vereinfache

\frac{125}{6} + \frac{125}{6} : \frac{125}{3}

= \frac{125}{3}

\int_{1}^{5} (6 - x) d x

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