Question

If $\left[y\right]$ denotes the greatest integer less than or equal to $y$ for all $y\in R$, then the value of the integral $\underset{1/2}{\overset{13/2}{\int }}[\sqrt{x}]dx$ is

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is A $8$

$\underset{1/2}{\overset{13/2}{\int }}\left[\sqrt{x}\right]dx$
$=\underset{1/2}{\overset{1}{\int }}0dx+\underset{1}{\overset{4}{\int }}1dx+\underset{4}{\overset{13/2}{\int }}2dx=3+2(\frac{13}{2}-4)=3+5=8$