integral from 0 to 3 of x(x-7)

解

\int_{0}^{3} x (x - 7) d x

- \frac{45}{2}

十進法表記

- 22.5

解答ステップ

\int_{0}^{3} x (x - 7) d x

拡張

x (x - 7) : x^{2} - 7 x

= \int_{0}^{3} x^{2} - 7 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_{0}^{3} x^{2} d x - \int_{0}^{3} 7 x d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 7 x d x = \frac{63}{2}

= 9 - \frac{63}{2}

簡素化

9 - \frac{63}{2} : - \frac{45}{2}

= - \frac{45}{2}