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

Lösung

\int_{- 1}^{1} x^{2} ln ∣ x ∣ d x

- \frac{2}{9}

Dezimale

- 0.22222 \dots

Schritte zur Lösung

\int_{- 1}^{1} x^{2} ln ∣ x ∣ d x

Entferne die Extremwerte

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

\int_{- 1}^{0} x^{2} ln (- x) d x = - \frac{1}{9}

\int_{0}^{1} x^{2} ln (x) d x = - \frac{1}{9}

= - \frac{1}{9} - \frac{1}{9}

Vereinfache

- \frac{1}{9} - \frac{1}{9} : - \frac{2}{9}

= - \frac{2}{9}

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