integral from-2 to 0 of x^4-2x^2

解

\int_{- 2}^{0} x^{4} - 2 x^{2} d x

\frac{16}{15}

十進法表記

1.06666 \dots

解答ステップ

\int_{- 2}^{0} x^{4} - 2 x^{2} 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_{- 2}^{0} x^{4} d x - \int_{- 2}^{0} 2 x^{2} d x

\int_{- 2}^{0} x^{4} d x = \frac{32}{5}

\int_{- 2}^{0} 2 x^{2} d x = \frac{16}{3}

= \frac{32}{5} - \frac{16}{3}

簡素化

\frac{32}{5} - \frac{16}{3} : \frac{16}{15}

= \frac{16}{15}