What is the integral from-3 to-2 of x^2+5x+6 ?

The integral from-3 to-2 of x^2+5x+6 is -1/6

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integral from-3 to-2 of x^2+5x+6

\int_{- 3}^{- 2} x^{2} + 5 x + 6 d x

- \frac{1}{6}

Decimal

- 0.16666 \dots

Solution steps

\int_{- 3}^{- 2} x^{2} + 5 x + 6 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_{- 3}^{- 2} x^{2} d x + \int_{- 3}^{- 2} 5 x d x + \int_{- 3}^{- 2} 6 d x

\int_{- 3}^{- 2} x^{2} d x = \frac{19}{3}

\int_{- 3}^{- 2} 5 x d x = - \frac{25}{2}

\int_{- 3}^{- 2} 6 d x = 6

= \frac{19}{3} - \frac{25}{2} + 6

Simplify

\frac{19}{3} - \frac{25}{2} + 6 : - \frac{1}{6}

= - \frac{1}{6}

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What is the integral from-3 to-2 of x^2+5x+6 ?
The integral from-3 to-2 of x^2+5x+6 is -1/6