Question

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

Answer 1

Correct Answer: 22

The correct answer is 22.
$12\underset{0}{\overset{3}{\int }}\left|x^2-3x+2\right|dx$
$=12\underset{0}{\overset{3}{\int }}\left|{\left(x-\frac{3}{2}\right)}^2-\frac{1}{4}\right|dx$
$\text{If}x-\frac{3}{2}=t$
$dx-dt$
$=24\underset{0}{\overset{3/2}{\int }}\left|t^2-\frac{1}{4}\right|dt$
$=24\left[-\underset{0}{\overset{1/2}{\int }}\left(t^2-\frac{1}{4}\right)dt+\underset{1/2}{\overset{3/2}{\int }}\left(t^2-\frac{1}{4}\right)dt\right]=22$