integral from 2 to 6 of 2x^2-16x+24

解

\int_{2}^{6} 2 x^{2} - 16 x + 24 d x

- \frac{64}{3}

十進法表記

- 21.33333 \dots

解答ステップ

\int_{2}^{6} 2 x^{2} - 16 x + 24 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}^{6} 2 x^{2} d x - \int_{2}^{6} 16 x d x + \int_{2}^{6} 24 d x

\int_{2}^{6} 2 x^{2} d x = \frac{416}{3}

\int_{2}^{6} 16 x d x = 256

\int_{2}^{6} 24 d x = 96

= \frac{416}{3} - 256 + 96

簡素化

\frac{416}{3} - 256 + 96 : - \frac{64}{3}

= - \frac{64}{3}