integral from-27 to 125 of 1/(x^{1/3)}

Lösung

\int_{- 27}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

24

Schritte zur Lösung

\int_{- 27}^{125} \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_{- 27}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{- 27}^{0} \frac{1}{x ^{\frac{1}{3}}} d x = - \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2}

\int_{0}^{125} \frac{1}{x ^{\frac{1}{3}}} d x = \frac{75}{2}

= - \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{75}{2}

Vereinfache

- \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{75}{2} : 24

= 24

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