integral from-3 to 3 of x^4-x^2+20

解

\int_{- 3}^{3} x^{4} - x^{2} + 20 d x

\frac{996}{5}

十進法表記

199.2

解答ステップ

\int_{- 3}^{3} x^{4} - x^{2} + 20 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_{- 3}^{3} x^{4} d x - \int_{- 3}^{3} x^{2} d x + \int_{- 3}^{3} 20 d x

\int_{- 3}^{3} x^{4} d x = \frac{486}{5}

\int_{- 3}^{3} x^{2} d x = 18

\int_{- 3}^{3} 20 d x = 120

= \frac{486}{5} - 18 + 120

簡素化

\frac{486}{5} - 18 + 120 : \frac{996}{5}

= \frac{996}{5}