integral from-2 to 1 of (3x^3-2x^2+x)

解

\int_{- 2}^{1} (3 x^{3} - 2 x^{2} + x) d x

- \frac{75}{4}

十進法表記

- 18.75

解答ステップ

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

\int_{- 2}^{1} 3 x^{3} d x = - \frac{45}{4}

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

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

= - \frac{45}{4} - 6 - \frac{3}{2}

簡素化

- \frac{45}{4} - 6 - \frac{3}{2} : - \frac{75}{4}

= - \frac{75}{4}