integral from 0 to 6 of 2piy(36-y^2)

Lösung

\int_{0}^{6} 2 π y (36 - y^{2}) d y

648 π

Dezimale

2035.75203 \dots

Schritte zur Lösung

\int_{0}^{6} 2 π y (36 - y^{2}) d y

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{6} y (36 - y^{2}) d y

Multipliziere aus

y (36 - y^{2}) : 36 y - y^{3}

= 2 π \cdot \int_{0}^{6} 36 y - y^{3} d y

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} 36 y d y - \int_{0}^{6} y^{3} d y)

\int_{0}^{6} 36 y d y = 648

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

= 2 π (648 - 324)

Vereinfache

= 648 π

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