integral from-2 to 1 of x^3-2x^2-5x+6

解

\int_{- 2}^{1} x^{3} - 2 x^{2} - 5 x + 6 d x

\frac{63}{4}

十進法表記

15.75

解答ステップ

\int_{- 2}^{1} x^{3} - 2 x^{2} - 5 x + 6 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}^{1} x^{3} d x - \int_{- 2}^{1} 2 x^{2} d x - \int_{- 2}^{1} 5 x d x + \int_{- 2}^{1} 6 d x

\int_{- 2}^{1} x^{3} d x = - \frac{15}{4}

\int_{- 2}^{1} 2 x^{2} d x = 6

\int_{- 2}^{1} 5 x d x = - \frac{15}{2}

\int_{- 2}^{1} 6 d x = 18

= - \frac{15}{4} - 6 - (- \frac{15}{2}) + 18

簡素化

- \frac{15}{4} - 6 - (- \frac{15}{2}) + 18 : \frac{63}{4}

= \frac{63}{4}