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Beliebt Rechnen >

integral from 0 to 8 of 2pix(x^{2/3})

Lösung

\int_{0}^{8} 2 π x (x^{\frac{2}{3}}) d x

Lösung

192 π

+1

Dezimale

603.18578 \dots

Schritte zur Lösung

\int_{0}^{8} 2 π x x^{\frac{2}{3}} d x

Entferne die Konstante:

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

= 2 π \cdot \int_{0}^{8} x x^{\frac{2}{3}} d x

Vereinfache

x x^{\frac{2}{3}} : x^{\frac{5}{3}}

= 2 π \cdot \int_{0}^{8} x^{\frac{5}{3}} d x

Wende die Potenzregel an

= 2 π [\frac{3}{8} x^{\frac{8}{3}}]_{0}^{8}

Berechne die Grenzen:

96

= 2 π 96

Vereinfache

= 192 π

Graph

Beliebte Beispiele

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