What is the integral from 1 to 5 of |x^2-2x-8| ?

The integral from 1 to 5 of |x^2-2x-8| is 64/3

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integral from 1 to 5 of |x^2-2x-8|

\int_{1}^{5} x^{2} - 2 x - 8 d x

\frac{64}{3}

Decimal

21.33333 \dots

Solution steps

\int_{1}^{5} x^{2} - 2 x - 8 d x

Eliminate Absolutes

= \int_{1}^{4} - x^{2} + 2 x + 8 d x + \int_{4}^{5} x^{2} - 2 x - 8 d x

\int_{1}^{4} - x^{2} + 2 x + 8 d x = 18

\int_{4}^{5} x^{2} - 2 x - 8 d x = \frac{10}{3}

= 18 + \frac{10}{3}

Simplify

18 + \frac{10}{3} : \frac{64}{3}

= \frac{64}{3}

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What is the integral from 1 to 5 of |x^2-2x-8| ?
The integral from 1 to 5 of |x^2-2x-8| is 64/3