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Beliebt Rechnen >

integral from 0 to 9 of 3/(\sqrt[3]{x-1)}

Lösung

\int_{0}^{9} \frac{3}{3 x - 1} d x

Lösung

\frac{27}{2}

+1

Dezimale

13.5

Schritte zur Lösung

\int_{0}^{9} \frac{3}{3 x - 1} 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{3}{3 x - 1} d x + \int_{1}^{9} \frac{3}{3 x - 1} d x

\int_{0}^{1} \frac{3}{3 x - 1} d x = - \frac{9 ( - 1 ) ^{\frac{2}{3}}}{2}

\int_{1}^{9} \frac{3}{3 x - 1} d x = 18

= - \frac{9 ( - 1 ) ^{\frac{2}{3}}}{2} + 18

Vereinfache

- \frac{9 ( - 1 ) ^{\frac{2}{3}}}{2} + 18 : \frac{27}{2}

= \frac{27}{2}

Graph

Beliebte Beispiele

derivative f(4)=4x^{5/4}+8x^{3/2}+8x

d er i v a t i v e f (4) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 8 x

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\frac{d ^{2}}{d x ^{2}} (sec (θ))

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\int_{- \infty}^{0} e^{- 3 x} d x

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