integral from 4 to 16 of (x-1)sqrt(x)

解

\int_{4}^{16} (x - 1) x d x

\frac{5392}{15}

十進法表記

359.46666 \dots

解答ステップ

\int_{4}^{16} (x - 1) x d x

拡張

(x - 1) x : x^{\frac{3}{2}} - x

= \int_{4}^{16} x^{\frac{3}{2}} - 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_{4}^{16} x^{\frac{3}{2}} d x - \int_{4}^{16} x d x

\int_{4}^{16} x^{\frac{3}{2}} d x = \frac{1984}{5}

\int_{4}^{16} x d x = \frac{112}{3}

= \frac{1984}{5} - \frac{112}{3}

簡素化

\frac{1984}{5} - \frac{112}{3} : \frac{5392}{15}

= \frac{5392}{15}