What is the integral from 0 to 500 of 6(700y-y^2) ?

The integral from 0 to 500 of 6(700y-y^2) is 275000000

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integral from 0 to 500 of 6(700y-y^2)

\int_{0}^{500} 6 (700 y - y^{2}) d y

275000000

Solution steps

\int_{0}^{500} 6 (700 y - y^{2}) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{0}^{500} 700 y - y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 6 (\int_{0}^{500} 700 y d y - \int_{0}^{500} y^{2} d y)

\int_{0}^{500} 700 y d y = 87500000

\int_{0}^{500} y^{2} d y = \frac{125000000}{3}

= 6 (87500000 - \frac{125000000}{3})

Simplify

6 (87500000 - \frac{125000000}{3}) : 275000000

= 275000000

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What is the integral from 0 to 500 of 6(700y-y^2) ?
The integral from 0 to 500 of 6(700y-y^2) is 275000000