integral from 0 to 1 of [(x^2+2)-(-x)]

解

\int_{0}^{1} [(x^{2} + 2) - (- x)] d x

\frac{17}{6}

十進法表記

2.83333 \dots

解答ステップ

\int_{0}^{1} x^{2} + 2 - (- x) d x

簡素化

= \int_{0}^{1} x^{2} + 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_{0}^{1} x^{2} d x + \int_{0}^{1} 2 d x + \int_{0}^{1} x d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

\int_{0}^{1} 2 d x = 2

\int_{0}^{1} x d x = \frac{1}{2}

= \frac{1}{3} + 2 + \frac{1}{2}

簡素化

\frac{1}{3} + 2 + \frac{1}{2} : \frac{17}{6}

= \frac{17}{6}