What is the integral from 0 to 40 of q^2+10q-90 ?

The integral from 0 to 40 of q^2+10q-90 is 77200/3

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integral from 0 to 40 of q^2+10q-90

\int_{0}^{40} q^{2} + 10 q - 90 d q

\frac{77200}{3}

Decimal

25733.33333 \dots

Solution steps

\int_{0}^{40} q^{2} + 10 q - 90 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_{0}^{40} q^{2} d q + \int_{0}^{40} 10 q d q - \int_{0}^{40} 90 d q

\int_{0}^{40} q^{2} d q = \frac{64000}{3}

\int_{0}^{40} 10 q d q = 8000

\int_{0}^{40} 90 d q = 3600

= \frac{64000}{3} + 8000 - 3600

Simplify

\frac{64000}{3} + 8000 - 3600 : \frac{77200}{3}

= \frac{77200}{3}

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What is the integral from 0 to 40 of q^2+10q-90 ?
The integral from 0 to 40 of q^2+10q-90 is 77200/3