What is the integral from 0 to 2 of 2x|x^2-3x+2| ?

The integral from 0 to 2 of 2x|x^2-3x+2| is 1

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integral from 0 to 2 of 2x|x^2-3x+2|

\int_{0}^{2} 2 x x^{2} - 3 x + 2 d x

1

Solution steps

\int_{0}^{2} 2 x x^{2} - 3 x + 2 d x

Eliminate Absolutes

= \int_{0}^{1} 2 x (x^{2} - 3 x + 2) d x + \int_{1}^{2} 2 x (- x^{2} + 3 x - 2) d x

\int_{0}^{1} 2 x (x^{2} - 3 x + 2) d x = \frac{1}{2}

\int_{1}^{2} 2 x (- x^{2} + 3 x - 2) d x = \frac{1}{2}

= \frac{1}{2} + \frac{1}{2}

Simplify

\frac{1}{2} + \frac{1}{2} : 1

= 1

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What is the integral from 0 to 2 of 2x|x^2-3x+2| ?
The integral from 0 to 2 of 2x|x^2-3x+2| is 1