integral from-1 to 27 of 1/(x^{1/3)}

Lösung

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

12

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= 12

\int_{\frac{π}{2}}^{π} cos^{3} (x) d x

\int_{1.5}^{2} 1 + x^{3} d x

\int_{0}^{49} t d t

\int_{1}^{1} \frac{1}{4 x ^{2} - 9} d x

\int_{- \infty}^{1} 6 - w d w