integral from 0 to 7 of x^3-9x^2+20x

解

\int_{0}^{7} x^{3} - 9 x^{2} + 20 x d x

\frac{245}{4}

十進法表記

61.25

解答ステップ

\int_{0}^{7} x^{3} - 9 x^{2} + 20 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}^{7} x^{3} d x - \int_{0}^{7} 9 x^{2} d x + \int_{0}^{7} 20 x d x

\int_{0}^{7} x^{3} d x = \frac{2401}{4}

\int_{0}^{7} 9 x^{2} d x = 1029

\int_{0}^{7} 20 x d x = 490

= \frac{2401}{4} - 1029 + 490

簡素化

\frac{2401}{4} - 1029 + 490 : \frac{245}{4}

= \frac{245}{4}