Question

If $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ then the value of ${\int }_1^5[|x-3|]dx$ is :

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

Answer: (B)

2

$I={\int }_1^5[|x-3|]dx$
$\Rightarrow I={\int }_1^3[-(x-3\left)\right]dx+{\int }_3^5\left[\right(x-3\left)\right]dx$
$={\int }_1^{2}dx+{\int }_2^{3}0\cdot dx+{\int }_3^{4}0\cdot dx+{\int }_4^5=[x{]}_1^2+[x{]}_4^5$
$\Rightarrow I=(2-1)+(5-4)=2$