integral from-64 to 1 of 1/(x^{1/3)}

解

\int_{- 64}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

- \frac{45}{2}

十進法表記

- 22.5

解答ステップ

\int_{- 64}^{1} \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_{- 64}^{0} \frac{1}{x ^{\frac{1}{3}}} d x + \int_{0}^{1} \frac{1}{x ^{\frac{1}{3}}} d x

\int_{- 64}^{0} \frac{1}{x ^{\frac{1}{3}}} d x = - 24 (- 1)^{\frac{2}{3}}

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

= - 24 (- 1)^{\frac{2}{3}} + \frac{3}{2}

簡素化

- 24 (- 1)^{\frac{2}{3}} + \frac{3}{2} : - \frac{45}{2}

= - \frac{45}{2}