integral from 0 to 2 of pi(4y^2-y^4)

Lösung

\int_{0}^{2} π (4 y^{2} - y^{4}) d y

π \frac{64}{15}

Dezimale

13.40412 \dots

Schritte zur Lösung

\int_{0}^{2} π (4 y^{2} - y^{4}) d y

Entferne die Konstante:

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

= π \cdot \int_{0}^{2} 4 y^{2} - y^{4} 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

= π (\int_{0}^{2} 4 y^{2} d y - \int_{0}^{2} y^{4} d y)

\int_{0}^{2} 4 y^{2} d y = \frac{32}{3}

\int_{0}^{2} y^{4} d y = \frac{32}{5}

= π (\frac{32}{3} - \frac{32}{5})

Füge

\frac{32}{3} - \frac{32}{5}

zusammen:

\frac{64}{15}

= π \frac{64}{15}

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