What is the integral from-7 to 2 of (-x^2-3x) ?

The integral from-7 to 2 of (-x^2-3x) is -99/2

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integral from-7 to 2 of (-x^2-3x)

\int_{- 7}^{2} (- x^{2} - 3 x) d x

- \frac{99}{2}

Solution steps

\int_{- 7}^{2} - 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_{- 7}^{2} x^{2} d x - \int_{- 7}^{2} 3 x d x

\int_{- 7}^{2} x^{2} d x = 117

\int_{- 7}^{2} 3 x d x = - \frac{135}{2}

= - 117 - (- \frac{135}{2})

Simplify

- 117 - (- \frac{135}{2}) : - \frac{99}{2}

= - \frac{99}{2}

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What is the integral from-7 to 2 of (-x^2-3x) ?
The integral from-7 to 2 of (-x^2-3x) is -99/2