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Beliebt Rechnen >

integral from 0 to 8 of 2piy(64-y^2)

Lösung

\int_{0}^{8} 2 π y (64 - y^{2}) d y

Lösung

2048 π

+1

Dezimale

6433.98175 \dots

Schritte zur Lösung

\int_{0}^{8} 2 π y (64 - 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}^{8} y (64 - y^{2}) d y

Multipliziere aus

y (64 - y^{2}) : 64 y - y^{3}

= 2 π \cdot \int_{0}^{8} 64 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}^{8} 64 y d y - \int_{0}^{8} y^{3} d y)

\int_{0}^{8} 64 y d y = 2048

\int_{0}^{8} y^{3} d y = 1024

= 2 π (2048 - 1024)

Vereinfache

= 2048 π

Graph

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