integral from 1 to 3 of (2x^2-12x+13)

解

\int_{1}^{3} (2 x^{2} - 12 x + 13) d x

- \frac{14}{3}

十進法表記

- 4.66666 \dots

解答ステップ

\int_{1}^{3} 2 x^{2} - 12 x + 13 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}^{3} 2 x^{2} d x - \int_{1}^{3} 12 x d x + \int_{1}^{3} 13 d x

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 12 x d x = 48

\int_{1}^{3} 13 d x = 26

= \frac{52}{3} - 48 + 26

簡素化

\frac{52}{3} - 48 + 26 : - \frac{14}{3}

= - \frac{14}{3}