What is the integral from 0 to 3 of y^2-4y-2y+y^2 ?

The integral from 0 to 3 of y^2-4y-2y+y^2 is -9

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integral from 0 to 3 of y^2-4y-2y+y^2

\int_{0}^{3} y^{2} - 4 y - 2 y + y^{2} d y

- 9

Solution steps

\int_{0}^{3} y^{2} - 4 y - 2 y + y^{2} d y

Simplify

= \int_{0}^{3} 2 y^{2} - 6 y 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

= \int_{0}^{3} 2 y^{2} d y - \int_{0}^{3} 6 y d y

\int_{0}^{3} 2 y^{2} d y = 18

\int_{0}^{3} 6 y d y = 27

= 18 - 27

Simplify

= - 9

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What is the integral from 0 to 3 of y^2-4y-2y+y^2 ?
The integral from 0 to 3 of y^2-4y-2y+y^2 is -9