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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1024}{3}

+1

Dezimale

341.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

y^{2} (8 - y) : 8 y^{2} - y^{3}

= \int_{0}^{8} 8 y^{2} - 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

= \int_{0}^{8} 8 y^{2} d y - \int_{0}^{8} y^{3} d y

\int_{0}^{8} 8 y^{2} d y = \frac{4096}{3}

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

= \frac{4096}{3} - 1024

Vereinfache

\frac{4096}{3} - 1024 : \frac{1024}{3}

= \frac{1024}{3}

Graph

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