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Beliebt Rechnen >

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

Lösung

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

Lösung

6

Schritte zur Lösung

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

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 1

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

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

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

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

Vereinfache

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

= 6

Graph

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