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Beliebt Rechnen >

integral from 0 to 2 of x^2(x^3+1)^{3/2}

Lösung

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

Lösung

\frac{484}{15}

+1

Dezimale

32.26666 \dots

Schritte zur Lösung

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

Wende U-Substitution an

= \int_{1}^{9} \frac{u ^{\frac{3}{2}}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{1}^{9} u^{\frac{3}{2}} d u

Wende die Potenzregel an

= \frac{1}{3} [\frac{2}{5} u^{\frac{5}{2}}]_{1}^{9}

Berechne die Grenzen:

\frac{484}{5}

= \frac{1}{3} \cdot \frac{484}{5}

Vereinfache

= \frac{484}{15}

Graph

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