integral from-2 to 2 of (4x^3+6x^2-8x+5)

解

\int_{- 2}^{2} (4 x^{3} + 6 x^{2} - 8 x + 5) d x

52

解答ステップ

\int_{- 2}^{2} 4 x^{3} + 6 x^{2} - 8 x + 5 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}^{2} 4 x^{3} d x + \int_{- 2}^{2} 6 x^{2} d x - \int_{- 2}^{2} 8 x d x + \int_{- 2}^{2} 5 d x

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

\int_{- 2}^{2} 6 x^{2} d x = 32

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

\int_{- 2}^{2} 5 d x = 20

= 0 + 32 - 0 + 20

簡素化

= 52