Question

$\underset{0}{\overset{4}{\int }}[2x+5]dx$ equals to
(where $[\cdot ]$ denotes the greatest integer function)

• A. $18$
• B. $36$
• C. $9$
• D. $34$

Answer 1

The correct option is D $34$

$\underset{0}{\overset{4}{\int }}[2x+5]dx=\underset{0}{\overset{4}{\int }}\left(\right[2x]+5)dx$
$(\because [x+I]=[x]+I)$

$\text{Put}2x=t\Rightarrow 2dx=dt$
$=\frac{1}{2}\underset{0}{\overset{8}{\int }}\left[t\right]dt+5\times 4$

$=\frac{1}{2}\cdot \left[\frac{8\times 7}{2}\right]+20=34$