Question

The value of ${\int }_0^8|x-5|dx$ is

• A. $17$
• B. $12$
• C. $9$
• D. $18$

Answer 1

The correct option is A $17$

Let $I={\int }_0^8|x-5|dx$
$={\int }_0^5-(x-5)dx+{\int }_0^5(x-5)dx$
$={[-\frac{x^2}{2}+5x]}_0^5+{[\frac{x^2}{2}-5x]}_0^5$
$=-\frac{25}{2}+25+\frac{64}{2}-40-\frac{25}{2}+25$
$=25-8=17$