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

The integral from-4 to 0 of-y-(y^2+3y) is 32/3

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

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

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

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

Simplify

= \int_{- 4}^{0} - y^{2} - 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_{- 4}^{0} y^{2} d y - \int_{- 4}^{0} 4 y d y

\int_{- 4}^{0} y^{2} d y = \frac{64}{3}

\int_{- 4}^{0} 4 y d y = - 32

= - \frac{64}{3} - (- 32)

Simplify

- \frac{64}{3} - (- 32) : \frac{32}{3}

= \frac{32}{3}

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What is the integral from-4 to 0 of-y-(y^2+3y) ?
The integral from-4 to 0 of-y-(y^2+3y) is 32/3