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

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

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

\frac{305}{6}

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}

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

\int_{0}^{2} 3 x + 1 d x

\int_{- 3}^{- 1} \frac{t + 1}{t ^{3}} d t

\int_{0}^{4} 6 x^{3} d x

\int_{1}^{e} \frac{1}{x ln ^{2} ( x )} d x

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