integral from-3 to-1 of-(3x^2)/5+x/5+6

解

\int_{- 3}^{- 1} - \frac{3 x ^{2}}{5} + \frac{x}{5} + 6 d x

6

解答ステップ

\int_{- 3}^{- 1} - \frac{3 x ^{2}}{5} + \frac{x}{5} + 6 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_{- 3}^{- 1} \frac{3 x ^{2}}{5} d x + \int_{- 3}^{- 1} \frac{x}{5} d x + \int_{- 3}^{- 1} 6 d x

\int_{- 3}^{- 1} \frac{3 x ^{2}}{5} d x = \frac{26}{5}

\int_{- 3}^{- 1} \frac{x}{5} d x = - \frac{4}{5}

\int_{- 3}^{- 1} 6 d x = 12

= - \frac{26}{5} - \frac{4}{5} + 12

簡素化

- \frac{26}{5} - \frac{4}{5} + 12 : 6

= 6