What is the integral from-1 to 5 of (y^2-5)-4y ?

The integral from-1 to 5 of (y^2-5)-4y is -36

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integral from-1 to 5 of (y^2-5)-4y

\int_{- 1}^{5} (y^{2} - 5) - 4 y d y

- 36

Solution steps

\int_{- 1}^{5} y^{2} - 5 - 4 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_{- 1}^{5} y^{2} d y - \int_{- 1}^{5} 5 d y - \int_{- 1}^{5} 4 y d y

\int_{- 1}^{5} y^{2} d y = 42

\int_{- 1}^{5} 5 d y = 30

\int_{- 1}^{5} 4 y d y = 48

= 42 - 30 - 48

Simplify

= - 36

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What is the integral from-1 to 5 of (y^2-5)-4y ?
The integral from-1 to 5 of (y^2-5)-4y is -36