What is the integral from-4 to 2 of (8-2x-x^2) ?

The integral from-4 to 2 of (8-2x-x^2) is 36

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integral from-4 to 2 of (8-2x-x^2)

\int_{- 4}^{2} (8 - 2 x - x^{2}) d x

36

Solution steps

\int_{- 4}^{2} 8 - 2 x - x^{2} d x

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}^{2} 8 d x - \int_{- 4}^{2} 2 x d x - \int_{- 4}^{2} x^{2} d x

\int_{- 4}^{2} 8 d x = 48

\int_{- 4}^{2} 2 x d x = - 12

\int_{- 4}^{2} x^{2} d x = 24

= 48 - (- 12) - 24

Simplify

= 36

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What is the integral from-4 to 2 of (8-2x-x^2) ?
The integral from-4 to 2 of (8-2x-x^2) is 36