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

解

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

\frac{95}{2}

十進法表記

47.5

解答ステップ

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

\int_{- 3}^{2} 3 x^{2} d x = 35

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

= 35 - (- \frac{25}{2})

簡素化

35 - (- \frac{25}{2}) : \frac{95}{2}

= \frac{95}{2}