integral from-3 to 2 of 4x^3-2x^2+x+5

解

\int_{- 3}^{2} 4 x^{3} - 2 x^{2} + x + 5 d x

- \frac{395}{6}

十進法表記

- 65.83333 \dots

解答ステップ

\int_{- 3}^{2} 4 x^{3} - 2 x^{2} + x + 5 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}^{2} 4 x^{3} d x - \int_{- 3}^{2} 2 x^{2} d x + \int_{- 3}^{2} x d x + \int_{- 3}^{2} 5 d x

\int_{- 3}^{2} 4 x^{3} d x = - 65

\int_{- 3}^{2} 2 x^{2} d x = \frac{70}{3}

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

\int_{- 3}^{2} 5 d x = 25

= - 65 - \frac{70}{3} - \frac{5}{2} + 25

簡素化

- 65 - \frac{70}{3} - \frac{5}{2} + 25 : - \frac{395}{6}

= - \frac{395}{6}