What is the integral from-3 to 1 of y^2-3-(-2y) ?

The integral from-3 to 1 of y^2-3-(-2y) is -32/3

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integral from-3 to 1 of y^2-3-(-2y)

\int_{- 3}^{1} y^{2} - 3 - (- 2 y) d y

- \frac{32}{3}

Decimal

- 10.66666 \dots

Solution steps

\int_{- 3}^{1} y^{2} - 3 - (- 2 y) d y

Simplify

= \int_{- 3}^{1} y^{2} - 3 + 2 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_{- 3}^{1} y^{2} d y - \int_{- 3}^{1} 3 d y + \int_{- 3}^{1} 2 y d y

\int_{- 3}^{1} y^{2} d y = \frac{28}{3}

\int_{- 3}^{1} 3 d y = 12

\int_{- 3}^{1} 2 y d y = - 8

= \frac{28}{3} - 12 - 8

Simplify

\frac{28}{3} - 12 - 8 : - \frac{32}{3}

= - \frac{32}{3}

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What is the integral from-3 to 1 of y^2-3-(-2y) ?
The integral from-3 to 1 of y^2-3-(-2y) is -32/3