integral from-2 to 6 of 4x-x^2-12

解

\int_{- 2}^{6} 4 x - x^{2} - 12 d x

- \frac{320}{3}

十進法表記

- 106.66666 \dots

解答ステップ

\int_{- 2}^{6} 4 x - x^{2} - 12 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} 4 x d x - \int_{- 2}^{6} x^{2} d x - \int_{- 2}^{6} 12 d x

\int_{- 2}^{6} 4 x d x = 64

\int_{- 2}^{6} x^{2} d x = \frac{224}{3}

\int_{- 2}^{6} 12 d x = 96

= 64 - \frac{224}{3} - 96

簡素化

64 - \frac{224}{3} - 96 : - \frac{320}{3}

= - \frac{320}{3}