integral from 0 to 5 of (5-x)^2

解

\int_{0}^{5} (5 - x)^{2} d x

\frac{125}{3}

十進法表記

41.66666 \dots

解答ステップ

\int_{0}^{5} (5 - x)^{2} d x

拡張

(5 - x)^{2} : 25 - 10 x + x^{2}

= \int_{0}^{5} 25 - 10 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}^{5} 25 d x - \int_{0}^{5} 10 x d x + \int_{0}^{5} x^{2} d x

\int_{0}^{5} 25 d x = 125

\int_{0}^{5} 10 x d x = 125

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= 125 - 125 + \frac{125}{3}

簡素化

= \frac{125}{3}