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

The integral from 2 to 3 of x^2-x-2 is 11/6

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

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

\frac{11}{6}

Solution steps

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

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

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

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

= \frac{19}{3} - \frac{5}{2} - 2

Simplify

\frac{19}{3} - \frac{5}{2} - 2 : \frac{11}{6}

= \frac{11}{6}

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What is the integral from 2 to 3 of x^2-x-2 ?
The integral from 2 to 3 of x^2-x-2 is 11/6