What is the integral from-1 to 3 of (-x^2-3x-2) ?

The integral from-1 to 3 of (-x^2-3x-2) is -88/3

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integral from-1 to 3 of (-x^2-3x-2)

\int_{- 1}^{3} (- x^{2} - 3 x - 2) d x

- \frac{88}{3}

Decimal

- 29.33333 \dots

Solution steps

\int_{- 1}^{3} - x^{2} - 3 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_{- 1}^{3} x^{2} d x - \int_{- 1}^{3} 3 x d x - \int_{- 1}^{3} 2 d x

\int_{- 1}^{3} x^{2} d x = \frac{28}{3}

\int_{- 1}^{3} 3 x d x = 12

\int_{- 1}^{3} 2 d x = 8

= - \frac{28}{3} - 12 - 8

Simplify

- \frac{28}{3} - 12 - 8 : - \frac{88}{3}

= - \frac{88}{3}

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What is the integral from-1 to 3 of (-x^2-3x-2) ?
The integral from-1 to 3 of (-x^2-3x-2) is -88/3