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Beliebt Rechnen >

integral from 0 to 6 of 2pix(6x-x^2)

Lösung

\int_{0}^{6} 2 π x (6 x - x^{2}) d x

Lösung

216 π

+1

Dezimale

678.58401 \dots

Schritte zur Lösung

\int_{0}^{6} 2 π x (6 x - x^{2}) d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{6} x (6 x - x^{2}) d x

Multipliziere aus

x (6 x - x^{2}) : 6 x^{2} - x^{3}

= 2 π \cdot \int_{0}^{6} 6 x^{2} - x^{3} 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

= 2 π (\int_{0}^{6} 6 x^{2} d x - \int_{0}^{6} x^{3} d x)

\int_{0}^{6} 6 x^{2} d x = 432

\int_{0}^{6} x^{3} d x = 324

= 2 π (432 - 324)

Vereinfache

= 216 π

Graph

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