integral from-1 to 0 of x^{1/3}-x^{2/3}

解

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

- \frac{27}{20}

十進法表記

- 1.35

解答ステップ

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

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 1}^{0} x^{\frac{1}{3}} d x = \frac{3 ( - 1 ) ^{\frac{1}{3}}}{4}

\int_{- 1}^{0} x^{\frac{2}{3}} d x = \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5}

= \frac{3 ( - 1 ) ^{\frac{1}{3}}}{4} - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5}

簡素化

\frac{3 ( - 1 ) ^{\frac{1}{3}}}{4} - \frac{3 ( - 1 ) ^{\frac{2}{3}}}{5} : - \frac{27}{20}

= - \frac{27}{20}