integral from-27 to 1 of 1/(\sqrt[3]{x)}

Lösung

\int_{- 27}^{1} \frac{1}{3 x} d x

- 12

Schritte zur Lösung

\int_{- 27}^{1} \frac{1}{3 x} 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_{- 27}^{0} \frac{1}{3 x} d x + \int_{0}^{1} \frac{1}{3 x} d x

\int_{- 27}^{0} \frac{1}{3 x} d x = - \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2}

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

= - \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{3}{2}

Vereinfache

- \frac{27 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{3}{2} : - 12

= - 12

d er i v a t i v e (2 x + 1) ln (x)

2 y d x + e^{- 3 x} d y = 0

\int \frac{x ^{2} + x - 5}{x ^{2} - 1} d x

\int \frac{5}{8 x ( x + 1 ) ^{2}} d x

\int - e^{- 2 y} + 1 d y