integral from-2 to 0 of 4x-x^2-6x

解

\int_{- 2}^{0} 4 x - x^{2} - 6 x d x

\frac{4}{3}

十進法表記

1.33333 \dots

解答ステップ

\int_{- 2}^{0} 4 x - x^{2} - 6 x d x

簡素化

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

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

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

= - \frac{8}{3} - (- 4)

簡素化

- \frac{8}{3} - (- 4) : \frac{4}{3}

= \frac{4}{3}