integral from 0 to-3 of-x^2-3x

解

\int_{0}^{- 3} - x^{2} - 3 x d x

- \frac{9}{2}

十進法表記

- 4.5

解答ステップ

\int_{0}^{- 3} - x^{2} - 3 x d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 3}^{0} - x^{2} - 3 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_{- 3}^{0} x^{2} d x - \int_{- 3}^{0} 3 x d x)

\int_{- 3}^{0} x^{2} d x = 9

\int_{- 3}^{0} 3 x d x = - \frac{27}{2}

= - (- 9 - (- \frac{27}{2}))

簡素化

- (- 9 - (- \frac{27}{2})) : - \frac{9}{2}

= - \frac{9}{2}