What is the integral from-6 to 4 of 24-2x-x^2 ?

The integral from-6 to 4 of 24-2x-x^2 is 500/3

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integral from-6 to 4 of 24-2x-x^2

\int_{- 6}^{4} 24 - 2 x - x^{2} d x

\frac{500}{3}

Solution steps

\int_{- 6}^{4} 24 - 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_{- 6}^{4} 24 d x - \int_{- 6}^{4} 2 x d x - \int_{- 6}^{4} x^{2} d x

\int_{- 6}^{4} 24 d x = 240

\int_{- 6}^{4} 2 x d x = - 20

\int_{- 6}^{4} x^{2} d x = \frac{280}{3}

= 240 - (- 20) - \frac{280}{3}

Simplify

240 - (- 20) - \frac{280}{3} : \frac{500}{3}

= \frac{500}{3}

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What is the integral from-6 to 4 of 24-2x-x^2 ?
The integral from-6 to 4 of 24-2x-x^2 is 500/3