integral from-2 to 2 of |x|-(6-x^2)

Lösung

\int_{- 2}^{2} ∣ x ∣ - (6 - x^{2}) d x

- \frac{44}{3}

Dezimale

- 14.66666 \dots

Schritte zur Lösung

\int_{- 2}^{2} ∣ x ∣ - (6 - x^{2}) d x

Entferne die Extremwerte

= \int_{- 2}^{0} - x - (6 - x^{2}) d x + \int_{0}^{2} x - (6 - x^{2}) d x

\int_{- 2}^{0} - x - (6 - x^{2}) d x = - \frac{22}{3}

\int_{0}^{2} x - (6 - x^{2}) d x = - \frac{22}{3}

= - \frac{22}{3} - \frac{22}{3}

Vereinfache

- \frac{22}{3} - \frac{22}{3} : - \frac{44}{3}

= - \frac{44}{3}

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