Question

$\int\limits_{0}^{8}| x -5| d x$ is equal to

• A. 17
• B. 9
• C. 12
• D. 18

Answer 1

Answer: (A)

17

Answer 2

By splitting $|x-5|$
$\Rightarrow x-5=[x-5, x \geq 5$
$[-x+5, x< 5$
$=\int\limits_{0}^{5}(-x+5) d x+\int\limits_{5}^{8}(x-5) d x$
$=\left[\frac{-x^{2}}{2}+5 x\right]_{0}^{5}+\left[\frac{-x^{2}}{2}-5 x\right]_{5}^{8}$
$=\frac{-25}{2}+25+\frac{64}{2}-25-40+25$
$=17$