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

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

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

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

- 36

Solution steps

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

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

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

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

= 24 - 12 - 48

Simplify

= - 36

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