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

The integral from-3 to 2 of 6-x^2-x is 125/6

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

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

\frac{125}{6}

Decimal

20.83333 \dots

Solution steps

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

\int_{- 3}^{2} 6 d x = 30

\int_{- 3}^{2} x^{2} d x = \frac{35}{3}

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

= 30 - \frac{35}{3} - (- \frac{5}{2})

Simplify

30 - \frac{35}{3} - (- \frac{5}{2}) : \frac{125}{6}

= \frac{125}{6}

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What is the integral from-3 to 2 of 6-x^2-x ?
The integral from-3 to 2 of 6-x^2-x is 125/6