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

The integral from-2 to 3 of |x^2-2x-3| is 13

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

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

13

Solution steps

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

Eliminate Absolutes

= \int_{- 2}^{- 1} x^{2} - 2 x - 3 d x + \int_{- 1}^{3} - x^{2} + 2 x + 3 d x

\int_{- 2}^{- 1} x^{2} - 2 x - 3 d x = \frac{7}{3}

\int_{- 1}^{3} - x^{2} + 2 x + 3 d x = \frac{32}{3}

= \frac{7}{3} + \frac{32}{3}

Simplify

\frac{7}{3} + \frac{32}{3} : 13

= 13

What is the integral from-2 to 3 of |x^2-2x-3| ?
The integral from-2 to 3 of |x^2-2x-3| is 13