integral from 0 to 2 of (x^2+21x)

解

\int_{0}^{2} (x^{2} + 21 x) d x

\frac{134}{3}

十進法表記

44.66666 \dots

解答ステップ

\int_{0}^{2} x^{2} + 21 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}^{2} x^{2} d x + \int_{0}^{2} 21 x d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 21 x d x = 42

= \frac{8}{3} + 42

簡素化

\frac{8}{3} + 42 : \frac{134}{3}

= \frac{134}{3}