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Beliebt Rechnen >

integral from-1 to 8 of 1/(x^{1/3)}

Lösung

\int_{- 1}^{8} \frac{1}{x ^{\frac{1}{3}}} d x

Lösung

\frac{9}{2}

+1

Dezimale

4.5

Schritte zur Lösung

\int_{- 1}^{8} \frac{1}{x ^{\frac{1}{3}}} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{8} \frac{1}{x ^{\frac{1}{3}}} d x

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

\int_{0}^{8} \frac{1}{x ^{\frac{1}{3}}} d x = 6

= - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 6

Vereinfache

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 6 : \frac{9}{2}

= \frac{9}{2}

Graph

Beliebte Beispiele

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\int_{2}^{7} 3 v d v

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\int_{0}^{π^{7}} 1