Question

The value of $\underset{2}{\overset{8}{\int }}|x-5|dx$ is

Answer 1

$I=\underset{2}{\overset{8}{\int }}|x-5|dx=\underset{2}{\overset{5}{\int }}(-x+5)dx+\underset{5}{\overset{8}{\int }}(x-5)dx={[5x-\frac{x^2}{2}]}_2^5+{[\frac{x^2}{2}-5x]}_5^8=9$