The value of 12 _0^3 |x^2-3 x+2 | d x is ............. - Vidyadip

Question

The value of $12 \int \limits_0^3\left|x^2-3 x+2\right| d x$ is $.............$

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Answer

c
$12 \int \limits_0^3\left| x ^2-3 x +2\right| dx$

$={ }_{12} \int_0^3\left|\left( x -\frac{3}{2}\right)^2-\frac{1}{4}\right| dx$

If $x-\frac{3}{2}=t$

$dx = dt$

$=24 \int \limits_0^{3 / 2}\left| t ^2-\frac{1}{4}\right| dt$

$=24\left[-\int^{1 / 2}\left(t^2-\frac{1}{4}\right) d t+\int \limits_0^{3 / 2}\left(t^2-\frac{1}{4}\right) d t\right]=22$

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