integral from 0 to 4 of (13-x)sqrt(x)

解

\int_{0}^{4} (13 - x) x d x

\frac{848}{15}

十進法表記

56.53333 \dots

解答ステップ

\int_{0}^{4} (13 - x) x d x

拡張

(13 - x) x : 13 x - x^{\frac{3}{2}}

= \int_{0}^{4} 13 x - x^{\frac{3}{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}^{4} 13 x d x - \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 13 x d x = \frac{208}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{208}{3} - \frac{64}{5}

簡素化

\frac{208}{3} - \frac{64}{5} : \frac{848}{15}

= \frac{848}{15}