integral from 0 to 7 of (7-x)^2

解

\int_{0}^{7} (7 - x)^{2} d x

\frac{343}{3}

十進法表記

114.33333 \dots

解答ステップ

\int_{0}^{7} (7 - x)^{2} d x

拡張

(7 - x)^{2} : 49 - 14 x + x^{2}

= \int_{0}^{7} 49 - 14 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}^{7} 49 d x - \int_{0}^{7} 14 x d x + \int_{0}^{7} x^{2} d x

\int_{0}^{7} 49 d x = 343

\int_{0}^{7} 14 x d x = 343

\int_{0}^{7} x^{2} d x = \frac{343}{3}

= 343 - 343 + \frac{343}{3}

簡素化

= \frac{343}{3}