Calculate the integral. ∫13|2x−4|dx

Step 1
Consider the provided integral,
${\displaystyle {\int }_1^3|2x-4|dx}$
Evaluate the provided integral.
The our function is defined at the point 2.
a<b<c : f(b)=undefined
So, ${\displaystyle {\int }_a^{c}f\left(x\right)dx={\int }_a^{b}f\left(x\right)dx+{\int }_b^{c}f\left(x\right)dx}$
Therefore,
${\displaystyle {\int }_1^3|2x-4|dx={\int }_1^2-2x+4dx+{\int }_2^{3}2x-4dx}$
Step 2
Simplifying further,
${\displaystyle {\int }_1^3|2x-4|dx={\int }_1^2-2x+4dx+{\int }_2^{3}2x-4dx}$
${\displaystyle =-{\left[x^2\right]}_1^2+4{\left[x\right]}_1^2+{\left[x^2\right]}_2^3-4{\left[x\right]}_2^3}$
=-[4-1]+4[2-1]+[9-4]-4[3-2]
=-3+4+5-4
=-3+5
=2
Hence.

${\displaystyle \int (2x-4)dx}$
${\displaystyle \int (2x-4)dx=x^2-4x}$
Lets

${\int }_1^3|2x-4|dx$
Transform
${\int }_1^2-(2x-4)dx+{\int }_2^{3}2x-4dx$
Evaluate
1+1
Answer:
2