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Beliebt Rechnen >

integral from 0 to 10 of 2piy(100-y^2)

Lösung

\int_{0}^{10} 2 π y (100 - y^{2}) d y

Lösung

5000 π

+1

Dezimale

15707.96326 \dots

Schritte zur Lösung

\int_{0}^{10} 2 π y (100 - 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}^{10} y (100 - y^{2}) d y

Multipliziere aus

y (100 - y^{2}) : 100 y - y^{3}

= 2 π \cdot \int_{0}^{10} 100 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}^{10} 100 y d y - \int_{0}^{10} y^{3} d y)

\int_{0}^{10} 100 y d y = 5000

\int_{0}^{10} y^{3} d y = 2500

= 2 π (5000 - 2500)

Vereinfache

= 5000 π

Graph

Beliebte Beispiele

integral of x^20.4^{-x}x

\int x^{2} 0. 4^{- x} x d x

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s l o p e in t erce pt (4, 5), (1, - 3)

t^2y^{''}-11ty^'+35y=0

t^{2} y^{^{''}} - 11 t y^{^{'}} + 35 y = 0

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\int \frac{x ^{4} + 8}{x ^{3}} d x

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