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Beliebt Rechnen >

integral from 2 to 6 of 7sqrt(x^3)

Lösung

\int_{2}^{6} 7 x^{3} d x

Lösung

\frac{7 ( 72 6 - 8 2 )}{5}

+1

Dezimale

231.06937 \dots

Schritte zur Lösung

\int_{2}^{6} 7 x^{3} d x

Entferne die Konstante:

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

= 7 \cdot \int_{2}^{6} x^{3} d x

x^{3} = x^{\frac{3}{2}},

angenommen

x \geq 0

= 7 \cdot \int_{2}^{6} x^{\frac{3}{2}} d x

Wende die Potenzregel an

= 7 [\frac{2}{5} x^{\frac{5}{2}}]_{2}^{6}

Berechne die Grenzen:

\frac{72 6 - 8 2}{5}

= 7 \cdot \frac{72 6 - 8 2}{5}

Vereinfache

= \frac{7 ( 72 6 - 8 2 )}{5}

Graph

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