integral from 0 to 3 of x-(x^2-2x)

解

\int_{0}^{3} x - (x^{2} - 2 x) d x

\frac{9}{2}

十進法表記

4.5

解答ステップ

\int_{0}^{3} x - (x^{2} - 2 x) d x

簡素化

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

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

\int_{0}^{3} 3 x d x = \frac{27}{2}

= - 9 + \frac{27}{2}

簡素化

- 9 + \frac{27}{2} : \frac{9}{2}

= \frac{9}{2}