integral from-125 to 125 of 1/(x^{1/3)}

解

\int_{- 125}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

0

解答ステップ

\int_{- 125}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

未定義の (特異) 点を求める:

x = 0

存在する場合は

b, a < b < c, f (b) =

未定義

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 125}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{125} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{- 125}^{0} \frac{1}{x ^{\frac{1}{3}}} d x = - \frac{75 ( - 1 ) ^{\frac{2}{3}}}{2}

\int_{0}^{125} \frac{1}{x ^{\frac{1}{3}}} d x = \frac{75}{2}

= - \frac{75 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{75}{2}

簡素化

- \frac{75 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{75}{2} : 0

= 0