integral from 1 to 5 of (x^2-x+1)

解

\int_{1}^{5} (x^{2} - x + 1) d x

\frac{100}{3}

十進法表記

33.33333 \dots

解答ステップ

\int_{1}^{5} x^{2} - x + 1 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}^{5} x^{2} d x - \int_{1}^{5} x d x + \int_{1}^{5} 1 d x

\int_{1}^{5} x^{2} d x = \frac{124}{3}

\int_{1}^{5} x d x = 12

\int_{1}^{5} 1 d x = 4

= \frac{124}{3} - 12 + 4

簡素化

\frac{124}{3} - 12 + 4 : \frac{100}{3}

= \frac{100}{3}