integral from 0 to 50 of (x^2-50x+700)

解

\int_{0}^{50} (x^{2} - 50 x + 700) d x

\frac{42500}{3}

十進法表記

14166.66666 \dots

解答ステップ

\int_{0}^{50} x^{2} - 50 x + 700 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}^{50} x^{2} d x - \int_{0}^{50} 50 x d x + \int_{0}^{50} 700 d x

\int_{0}^{50} x^{2} d x = \frac{125000}{3}

\int_{0}^{50} 50 x d x = 62500

\int_{0}^{50} 700 d x = 35000

= \frac{125000}{3} - 62500 + 35000

簡素化

\frac{125000}{3} - 62500 + 35000 : \frac{42500}{3}

= \frac{42500}{3}