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Beliebt Rechnen >

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

Lösung

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

Lösung

6

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= 6

Graph

Beliebte Beispiele

derivative of ((x+1/x)^3)

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

derivative of (x^2/(x^2-16))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

tangent f(x)=(13x-1)^{-1/3},\at x=5

t an g e n t f (x) = (13 x - 1)^{- \frac{1}{3}}, at x = 5

derivative t/((t-9)^2)

d er i v a t i v e \frac{t}{( t - 9 ) ^{2}}

25y^{''}+30y^'+9y=0

25 y^{^{''}} + 30 y^{^{'}} + 9 y = 0