integral from-3 to 0 of x^3+5x^2+6x

解

\int_{- 3}^{0} x^{3} + 5 x^{2} + 6 x d x

- \frac{9}{4}

十進法表記

- 2.25

解答ステップ

\int_{- 3}^{0} x^{3} + 5 x^{2} + 6 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^{3} d x + \int_{- 3}^{0} 5 x^{2} d x + \int_{- 3}^{0} 6 x d x

\int_{- 3}^{0} x^{3} d x = - \frac{81}{4}

\int_{- 3}^{0} 5 x^{2} d x = 45

\int_{- 3}^{0} 6 x d x = - 27

= - \frac{81}{4} + 45 - 27

簡素化

- \frac{81}{4} + 45 - 27 : - \frac{9}{4}

= - \frac{9}{4}