integral from 1 to 4 of-sqrt(x)-(2-x)

解

\int_{1}^{4} - x - (2 - x) d x

- \frac{19}{6}

十進法表記

- 3.16666 \dots

解答ステップ

\int_{1}^{4} - x - (2 - x) d x

簡素化

= \int_{1}^{4} - x - 2 + 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_{1}^{4} x d x - \int_{1}^{4} 2 d x + \int_{1}^{4} x d x

\int_{1}^{4} x d x = \frac{14}{3}

\int_{1}^{4} 2 d x = 6

\int_{1}^{4} x d x = \frac{15}{2}

= - \frac{14}{3} - 6 + \frac{15}{2}

簡素化

- \frac{14}{3} - 6 + \frac{15}{2} : - \frac{19}{6}

= - \frac{19}{6}