Question

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

• A. 27
• B. 30
• C. 29
• D. 28

Answer 1

The correct option is C 29

${\int }_{-5}^5|x+2|dx$
${\int }_{-5}^{-2}-(x+2)dx+{\int }_{-2}^5(x+2)dx$
$=-{\left|\frac{x^2}{2}\right|}_{-5}^{-2}-2{\left|x\right|}_{-5}^{-2}+{\left|\frac{x^2}{2}\right|}_{-2}^5+2{\left|x\right|}_{-2}^5$
$-[\frac{4}{2}-\frac{25}{2}]-2[-2+5]+[\frac{25}{2}-\frac{4}{2}]+2[5+2]$
$=\frac{21}{2}-6+\frac{21}{2}+14$
$=21+8$
$=29$