integral from 3 to 2 of (5x^2+4x+9)

解

\int_{3}^{2} (5 x^{2} + 4 x + 9) d x

- \frac{152}{3}

十進法表記

- 50.66666 \dots

解答ステップ

\int_{3}^{2} 5 x^{2} + 4 x + 9 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{2}^{3} 5 x^{2} + 4 x + 9 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}^{3} 5 x^{2} d x + \int_{2}^{3} 4 x d x + \int_{2}^{3} 9 d x)

\int_{2}^{3} 5 x^{2} d x = \frac{95}{3}

\int_{2}^{3} 4 x d x = 10

\int_{2}^{3} 9 d x = 9

= - (\frac{95}{3} + 10 + 9)

簡素化

- (\frac{95}{3} + 10 + 9) : - \frac{152}{3}

= - \frac{152}{3}