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Beliebt Rechnen >

integral from 1/4 to 7 of 9/(\sqrt[3]{4x-1)}

Lösung

\int_{\frac{1}{4}}^{7} \frac{9}{3 4 x - 1} d x

Lösung

\frac{243}{8}

+1

Dezimale

30.375

Schritte zur Lösung

\int_{\frac{1}{4}}^{7} \frac{9}{3 4 x - 1} d x

Entferne die Konstante:

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

= 9 \cdot \int_{\frac{1}{4}}^{7} \frac{1}{3 4 x - 1} d x

Wende U-Substitution an

= 9 \cdot \int_{0}^{27} \frac{1}{4 3 u} d u

Entferne die Konstante:

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

= 9 \cdot \frac{1}{4} \cdot \int_{0}^{27} \frac{1}{3 u} d u

Wende die Potenzregel an

= 9 \cdot \frac{1}{4} [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{27}

Vereinfache

9 \cdot \frac{1}{4} [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{27} : \frac{9}{4} [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{27}

= \frac{9}{4} [\frac{3}{2} u^{\frac{2}{3}}]_{0}^{27}

Berechne die Grenzen:

\frac{27}{2}

= \frac{9}{4} \cdot \frac{27}{2}

Vereinfache

= \frac{243}{8}

Graph

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