integral from-5 to 0 of 2+sqrt(4-x)+x

解

\int_{- 5}^{0} 2 + 4 - x + x d x

\frac{61}{6}

十進法表記

10.16666 \dots

解答ステップ

\int_{- 5}^{0} 2 + 4 - 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_{- 5}^{0} 2 d x + \int_{- 5}^{0} 4 - x d x + \int_{- 5}^{0} x d x

\int_{- 5}^{0} 2 d x = 10

\int_{- 5}^{0} 4 - x d x = \frac{38}{3}

\int_{- 5}^{0} x d x = - \frac{25}{2}

= 10 + \frac{38}{3} - \frac{25}{2}

簡素化

10 + \frac{38}{3} - \frac{25}{2} : \frac{61}{6}

= \frac{61}{6}