integral from-2 to 2 of x^4+5x^2+2x+8

解

\int_{- 2}^{2} x^{4} + 5 x^{2} + 2 x + 8 d x

\frac{1072}{15}

十進法表記

71.46666 \dots

解答ステップ

\int_{- 2}^{2} x^{4} + 5 x^{2} + 2 x + 8 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}^{2} x^{4} d x + \int_{- 2}^{2} 5 x^{2} d x + \int_{- 2}^{2} 2 x d x + \int_{- 2}^{2} 8 d x

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

\int_{- 2}^{2} 5 x^{2} d x = \frac{80}{3}

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

\int_{- 2}^{2} 8 d x = 32

= \frac{64}{5} + \frac{80}{3} + 0 + 32

簡素化

\frac{64}{5} + \frac{80}{3} + 0 + 32 : \frac{1072}{15}

= \frac{1072}{15}