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

The integral from 8 to 6 of ((q^2)/4-5q+25) is -14/3

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

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

- \frac{14}{3}

Decimal

- 4.66666 \dots

Solution steps

\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

Apply the Sum Rule:

\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)

Simplify

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

= - \frac{14}{3}

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What is the integral from 8 to 6 of ((q^2)/4-5q+25) ?
The integral from 8 to 6 of ((q^2)/4-5q+25) is -14/3