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

解

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

\frac{1}{6}

十進法表記

0.16666 \dots

解答ステップ

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

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

\int_{1}^{2} 3 x d x = \frac{9}{2}

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

= - \frac{7}{3} + \frac{9}{2} - 2

簡素化

- \frac{7}{3} + \frac{9}{2} - 2 : \frac{1}{6}

= \frac{1}{6}