integral from-3 to 0 of x^2-4x+7

解

\int_{- 3}^{0} x^{2} - 4 x + 7 d x

48

解答ステップ

\int_{- 3}^{0} x^{2} - 4 x + 7 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} 4 x d x + \int_{- 3}^{0} 7 d x

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

\int_{- 3}^{0} 4 x d x = - 18

\int_{- 3}^{0} 7 d x = 21

= 9 - (- 18) + 21

簡素化

= 48