integral from-1 to 2 of (|x|(x^2-1))/x

Lösung

\int_{- 1}^{2} \frac{∣ x ∣ ( x ^{2} - 1 )}{x} d x

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{- 1}^{2} \frac{∣ x ∣ ( x ^{2} - 1 )}{x} d x

Entferne die Extremwerte

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

\int_{- 1}^{0} \frac{( - x ) ( x ^{2} - 1 )}{x} d x = \frac{2}{3}

\int_{0}^{2} \frac{x ( x ^{2} - 1 )}{x} d x = \frac{2}{3}

= \frac{2}{3} + \frac{2}{3}

Vereinfache

\frac{2}{3} + \frac{2}{3} : \frac{4}{3}

= \frac{4}{3}

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