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Beliebt Rechnen >

integral from 0 to 1 of 2pi2/3x*2/3

Lösung

\int_{0}^{1} 2 π \cdot \frac{2}{3} \cdot x \cdot \frac{2}{3} d x

Lösung

\frac{4 π}{9}

+1

Dezimale

1.39626 \dots

Schritte zur Lösung

\int_{0}^{1} 2 π \frac{2}{3} 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 \frac{2}{3} \cdot \frac{2}{3} \cdot \int_{0}^{1} x d x

2 π \frac{2}{3} \cdot \frac{2}{3} = \frac{8 π}{9}

= \frac{8 π}{9} \cdot \int_{0}^{1} x d x

Wende die Potenzregel an

= \frac{8 π}{9} [\frac{x ^{2}}{2}]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= \frac{8 π}{9} \cdot \frac{1}{2}

Vereinfache

= \frac{4 π}{9}

Graph

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