integral from 0 to 2 of (2-x)^2

解

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

\frac{8}{3}

十進法表記

2.66666 \dots

解答ステップ

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

拡張

(2 - x)^{2} : 4 - 4 x + x^{2}

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

\int_{0}^{2} 4 d x = 8

\int_{0}^{2} 4 x d x = 8

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

= 8 - 8 + \frac{8}{3}

簡素化

= \frac{8}{3}