What is the integral from-8 to 4 of (-x^2-3x) ?

The integral from-8 to 4 of (-x^2-3x) is -120

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integral from-8 to 4 of (-x^2-3x)

\int_{- 8}^{4} (- x^{2} - 3 x) d x

- 120

Solution steps

\int_{- 8}^{4} - x^{2} - 3 x 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_{- 8}^{4} x^{2} d x - \int_{- 8}^{4} 3 x d x

\int_{- 8}^{4} x^{2} d x = 192

\int_{- 8}^{4} 3 x d x = - 72

= - 192 - (- 72)

Simplify

= - 120

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What is the integral from-8 to 4 of (-x^2-3x) ?
The integral from-8 to 4 of (-x^2-3x) is -120