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

解

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

\frac{3}{2}

十進法表記

1.5

解答ステップ

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

\int_{1}^{2} 3 x^{2} d x = 7

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

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

= 7 - \frac{15}{2} + 2

簡素化

7 - \frac{15}{2} + 2 : \frac{3}{2}

= \frac{3}{2}