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

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

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

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

\frac{99}{2}

Decimal

49.5

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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