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

解

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

32

解答ステップ

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

\int_{- 4}^{0} 3 x^{2} d x = 64

\int_{- 4}^{0} x^{3} d x = - 64

\int_{- 4}^{0} 4 x d x = - 32

= 64 - 64 - (- 32)

簡素化

= 32