integral from 1 to 5 of x^2+x+2

解

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

\frac{184}{3}

十進法表記

61.33333 \dots

解答ステップ

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

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

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

\int_{1}^{5} 2 d x = 8

= \frac{124}{3} + 12 + 8

簡素化

\frac{124}{3} + 12 + 8 : \frac{184}{3}

= \frac{184}{3}