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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{3}{2} + \frac{3 \cdot 3 ^{\frac{1}{3}}}{2}

+1

Dezimale

3.66337 \dots

Schritte zur Lösung

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

Bestimme unbestimmte (Singularitäts-)Punkte:

x = \frac{1}{2}

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

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

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

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

Vereinfache

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

= \frac{3}{2} + \frac{3 \cdot 3 ^{\frac{1}{3}}}{2}

Graph

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