What is the integral from-3 to 2 of (12-x^2-x) ?

The integral from-3 to 2 of (12-x^2-x) is 305/6

integral from-3 to 2 of (12-x^2-x)

\int_{- 3}^{2} (12 - x^{2} - x) d x

\frac{305}{6}

Decimal

50.83333 \dots

Solution steps

\int_{- 3}^{2} 12 - 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} 12 d x - \int_{- 3}^{2} x^{2} d x - \int_{- 3}^{2} x d x

\int_{- 3}^{2} 12 d x = 60

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

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

= 60 - \frac{35}{3} - (- \frac{5}{2})

Simplify

60 - \frac{35}{3} - (- \frac{5}{2}) : \frac{305}{6}

= \frac{305}{6}

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What is the integral from-3 to 2 of (12-x^2-x) ?
The integral from-3 to 2 of (12-x^2-x) is 305/6