integral from 0 to 20 of q^2-13q+70

解

\int_{0}^{20} q^{2} - 13 q + 70 d q

\frac{4400}{3}

十進法表記

1466.66666 \dots

解答ステップ

\int_{0}^{20} q^{2} - 13 q + 70 d q

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} q^{2} d q - \int_{0}^{20} 13 q d q + \int_{0}^{20} 70 d q

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

\int_{0}^{20} 13 q d q = 2600

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

= \frac{8000}{3} - 2600 + 1400

簡素化

\frac{8000}{3} - 2600 + 1400 : \frac{4400}{3}

= \frac{4400}{3}