integral from-pi to pi of pi^2-x^2

Lösung

\int_{- π}^{π} π^{2} - x^{2} d x

2 π^{3} - \frac{2 π ^{3}}{3}

Dezimale

41.34170 \dots

Schritte zur Lösung

\int_{- π}^{π} π^{2} - x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- π}^{π} π^{2} d x = 2 π^{3}

\int_{- π}^{π} x^{2} d x = \frac{2 π ^{3}}{3}

= 2 π^{3} - \frac{2 π ^{3}}{3}

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