What is the integral from 1 to 4 of |x^2-5x+6| ?

The integral from 1 to 4 of |x^2-5x+6| is 11/6

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integral from 1 to 4 of |x^2-5x+6|

\int_{1}^{4} x^{2} - 5 x + 6 d x

\frac{11}{6}

Decimal

1.83333 \dots

Solution steps

\int_{1}^{4} x^{2} - 5 x + 6 d x

Eliminate Absolutes

= \int_{1}^{2} x^{2} - 5 x + 6 d x + \int_{2}^{3} - x^{2} + 5 x - 6 d x + \int_{3}^{4} x^{2} - 5 x + 6 d x

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

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

\int_{3}^{4} x^{2} - 5 x + 6 d x = \frac{5}{6}

= \frac{5}{6} + \frac{1}{6} + \frac{5}{6}

Simplify

\frac{5}{6} + \frac{1}{6} + \frac{5}{6} : \frac{11}{6}

= \frac{11}{6}

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What is the integral from 1 to 4 of |x^2-5x+6| ?
The integral from 1 to 4 of |x^2-5x+6| is 11/6