Question

Evaluate: ${\int }_{-5}^5|x+2|dx$

Answer 1

${\int }_{-5}5|x+2|dx={\int }_{-5}^0|x+2|dx+{\int }_0^5|x+2|dx$

$|x+2|>0$ if $x>0$

$|x+2|<0$ if $x<0$

$=[-\frac{x^2}{2}-2x{]}_{-5}^0+[\frac{x^2}{2}+2x{]}_0^5$

$=\frac{5}{2}+\frac{45}{2}=25$