What is the integral from 0 to 9 of |x^2-6x+5| ?

The integral from 0 to 9 of |x^2-6x+5| is 199/3

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integral from 0 to 9 of |x^2-6x+5|

\int_{0}^{9} x^{2} - 6 x + 5 d x

\frac{199}{3}

Decimal Notation

66.33333 \dots

Solution steps

\int_{0}^{9} x^{2} - 6 x + 5 d x

Eliminate Absolutes

= \int_{0}^{1} x^{2} - 6 x + 5 d x + \int_{1}^{5} - x^{2} + 6 x - 5 d x + \int_{5}^{9} x^{2} - 6 x + 5 d x

\int_{0}^{1} x^{2} - 6 x + 5 d x = \frac{7}{3}

\int_{1}^{5} - x^{2} + 6 x - 5 d x = \frac{32}{3}

\int_{5}^{9} x^{2} - 6 x + 5 d x = \frac{160}{3}

= \frac{7}{3} + \frac{32}{3} + \frac{160}{3}

Simplify

\frac{7}{3} + \frac{32}{3} + \frac{160}{3} : \frac{199}{3}

= \frac{199}{3}

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What is the integral from 0 to 9 of |x^2-6x+5| ?
The integral from 0 to 9 of |x^2-6x+5| is 199/3