integral from 8 to 6 of ((q^2)/4-5q+25)

解

\int_{8}^{6} (\frac{q ^{2}}{4} - 5 q + 25) d q

- \frac{14}{3}

十進法表記

- 4.66666 \dots

解答ステップ

\int_{8}^{6} \frac{q ^{2}}{4} - 5 q + 25 d q

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{6}^{8} \frac{q ^{2}}{4} - 5 q + 25 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_{6}^{8} \frac{q ^{2}}{4} d q - \int_{6}^{8} 5 q d q + \int_{6}^{8} 25 d q)

\int_{6}^{8} \frac{q ^{2}}{4} d q = \frac{74}{3}

\int_{6}^{8} 5 q d q = 70

\int_{6}^{8} 25 d q = 50

= - (\frac{74}{3} - 70 + 50)

簡素化

- (\frac{74}{3} - 70 + 50) : - \frac{14}{3}

= - \frac{14}{3}