integral from 0 to 20 of x^2-14x+70

解

\int_{0}^{20} x^{2} - 14 x + 70 d x

\frac{3800}{3}

十進法表記

1266.66666 \dots

解答ステップ

\int_{0}^{20} x^{2} - 14 x + 70 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}^{20} x^{2} d x - \int_{0}^{20} 14 x d x + \int_{0}^{20} 70 d x

\int_{0}^{20} x^{2} d x = \frac{8000}{3}

\int_{0}^{20} 14 x d x = 2800

\int_{0}^{20} 70 d x = 1400

= \frac{8000}{3} - 2800 + 1400

簡素化

\frac{8000}{3} - 2800 + 1400 : \frac{3800}{3}

= \frac{3800}{3}