integral from-pi to 0 of 6x^2

Lösung

\int_{- π}^{0} 6 x^{2} d x

2 π^{3}

Dezimale

62.01255 \dots

Schritte zur Lösung

\int_{- π}^{0} 6 x^{2} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{- π}^{0} x^{2} d x

Wende die Potenzregel an

= 6 [\frac{x ^{3}}{3}]_{- π}^{0}

Berechne die Grenzen:

\frac{π ^{3}}{3}

= 6 \cdot \frac{π ^{3}}{3}

Vereinfache

= 2 π^{3}

\int_{0}^{1} 6 x^{5} (4 - x^{6}) d x

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