integral from-4 to 0 of x^3-x^2-14x

解

\int_{- 4}^{0} x^{3} - x^{2} - 14 x d x

\frac{80}{3}

十進法表記

26.66666 \dots

解答ステップ

\int_{- 4}^{0} x^{3} - x^{2} - 14 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} x^{3} d x - \int_{- 4}^{0} x^{2} d x - \int_{- 4}^{0} 14 x d x

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

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

\int_{- 4}^{0} 14 x d x = - 112

= - 64 - \frac{64}{3} - (- 112)

簡素化

- 64 - \frac{64}{3} - (- 112) : \frac{80}{3}

= \frac{80}{3}