What is the integral from 0 to 8 of |x^2-6x+8| ?

The integral from 0 to 8 of |x^2-6x+8| is 136/3

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integral from 0 to 8 of |x^2-6x+8|

\int_{0}^{8} x^{2} - 6 x + 8 d x

\frac{136}{3}

Decimal

45.33333 \dots

Solution steps

\int_{0}^{8} x^{2} - 6 x + 8 d x

Eliminate Absolutes

= \int_{0}^{2} x^{2} - 6 x + 8 d x + \int_{2}^{4} - x^{2} + 6 x - 8 d x + \int_{4}^{8} x^{2} - 6 x + 8 d x

\int_{0}^{2} x^{2} - 6 x + 8 d x = \frac{20}{3}

\int_{2}^{4} - x^{2} + 6 x - 8 d x = \frac{4}{3}

\int_{4}^{8} x^{2} - 6 x + 8 d x = \frac{112}{3}

= \frac{20}{3} + \frac{4}{3} + \frac{112}{3}

Simplify

\frac{20}{3} + \frac{4}{3} + \frac{112}{3} : \frac{136}{3}

= \frac{136}{3}

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What is the integral from 0 to 8 of |x^2-6x+8| ?
The integral from 0 to 8 of |x^2-6x+8| is 136/3