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

解

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

\frac{19}{6}

十進法表記

3.16666 \dots

解答ステップ

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

簡素化

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

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

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

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

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

簡素化

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

= \frac{19}{6}