What is the integral from 0 to 6 of |x^2-7x+10| ?

The integral from 0 to 6 of |x^2-7x+10| is 15

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integral from 0 to 6 of |x^2-7x+10|

\int_{0}^{6} x^{2} - 7 x + 10 d x

15

Solution steps

\int_{0}^{6} x^{2} - 7 x + 10 d x

Eliminate Absolutes

= \int_{0}^{2} x^{2} - 7 x + 10 d x + \int_{2}^{5} - x^{2} + 7 x - 10 d x + \int_{5}^{6} x^{2} - 7 x + 10 d x

\int_{0}^{2} x^{2} - 7 x + 10 d x = \frac{26}{3}

\int_{2}^{5} - x^{2} + 7 x - 10 d x = \frac{9}{2}

\int_{5}^{6} x^{2} - 7 x + 10 d x = \frac{11}{6}

= \frac{26}{3} + \frac{9}{2} + \frac{11}{6}

Simplify

\frac{26}{3} + \frac{9}{2} + \frac{11}{6} : 15

= 15

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What is the integral from 0 to 6 of |x^2-7x+10| ?
The integral from 0 to 6 of |x^2-7x+10| is 15