Question

If $\left[x\right]$ denotes the greatest integer function, then he value of ${\int }_{0.5}^{4.5}\left[x\right]dx+{\int }_{-1}^1|x|dx$ is

• A. $8$
• B. $7$
• C. $9$
• D. $6$

Answer 1

Answer: (C)

$9$

${\int }_{0.5}^{4.5}\left[x\right]dx+{\int }_{-1}^1|x|dx={\int }_{0.5}^{1}0dx+{\int }_1^{2}1dx+{\int }_2^{3}2dx+{\int }_3^{4}3dx+{\int }_4^{4.5}4dx+2{\int }_0^{1}xdx$

$=1+2+3+4\times 0.5+[1^2-0^2]=9$