integral from-pi to pi of |x|

Lösung

\int_{- π}^{π} ∣ x ∣ d x

π^{2}

Dezimale

9.86960 \dots

Schritte zur Lösung

\int_{- π}^{π} ∣ x ∣ d x

Entferne die Extremwerte

= \int_{- π}^{0} - x d x + \int_{0}^{π} x d x

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

\int_{0}^{π} x d x = \frac{π ^{2}}{2}

= \frac{π ^{2}}{2} + \frac{π ^{2}}{2}

Vereinfache

\frac{π ^{2}}{2} + \frac{π ^{2}}{2} : π^{2}

= π^{2}

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