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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{4096 \cdot 2 ^{\frac{1}{2}} π}{7}

+1

Dezimale

2599.72121 \dots

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Potenzregel an

= 2 π [\frac{2}{7} x^{\frac{7}{2}}]_{0}^{8}

Berechne die Grenzen:

\frac{2048 \cdot 2 ^{\frac{1}{2}}}{7}

= 2 π \frac{2048 \cdot 2 ^{\frac{1}{2}}}{7}

Vereinfache

= \frac{4096 \cdot 2 ^{\frac{1}{2}} π}{7}

Graph

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