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Beliebt Rechnen >

integral from-1 to 512 of x^{-1/3}

Lösung

\int_{- 1}^{512} x^{- \frac{1}{3}} d x

Lösung

\frac{189}{2}

+1

Dezimale

94.5

Schritte zur Lösung

\int_{- 1}^{512} 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} x^{- \frac{1}{3}} d x + \int_{0}^{512} x^{- \frac{1}{3}} d x

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

\int_{0}^{512} x^{- \frac{1}{3}} d x = 96

= - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 96

Vereinfache

- \frac{3 ( - 1 ) ^{\frac{2}{3}}}{2} + 96 : \frac{189}{2}

= \frac{189}{2}

Graph

Beliebte Beispiele

integral from-1/2 to 1/2 of 1

\int_{- \frac{1}{2}}^{\frac{1}{2}} 1 d x

integral from 2 to 6 of 8/x

\int_{2}^{6} \frac{8}{x} d x

integral from-1 to 4 of x^4

\int_{- 1}^{4} x^{4} d x

integral from 0 to 2 of sqrt(4-t^2)

\int_{0}^{2} 4 - t^{2} d t

integral from 0 to 1 of x^2+3x

\int_{0}^{1} x^{2} + 3 x d x