integral from-1 to 2 of x(1+x^3)

解

\int_{- 1}^{2} x (1 + x^{3}) d x

\frac{81}{10}

十進法表記

8.1

解答ステップ

\int_{- 1}^{2} x (1 + x^{3}) d x

拡張

x (1 + x^{3}) : x + x^{4}

= \int_{- 1}^{2} x + x^{4} 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}^{2} x d x + \int_{- 1}^{2} x^{4} d x

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

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

= \frac{3}{2} + \frac{33}{5}

簡素化

\frac{3}{2} + \frac{33}{5} : \frac{81}{10}

= \frac{81}{10}