integral from-1 to 1 of-x^2|x|

Lösung

\int_{- 1}^{1} - x^{2} ∣ x ∣ d x

- \frac{1}{2}

Dezimale

- 0.5

Schritte zur Lösung

\int_{- 1}^{1} - x^{2} ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- 1}^{0} - x^{2} (- x) d x + \int_{0}^{1} - x^{2} x d x

\int_{- 1}^{0} - x^{2} (- x) d x = - \frac{1}{4}

\int_{0}^{1} - x^{2} x d x = - \frac{1}{4}

= - \frac{1}{4} - \frac{1}{4}

Vereinfache

- \frac{1}{4} - \frac{1}{4} : - \frac{1}{2}

= - \frac{1}{2}

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