Question

${\int }_0^{1004}\left[ta{n}^{-1}x\right]dx$ equals, where [.]denotes greatest integer function

• A. $tan1$
• B. $1004-tan1$
• C. $\frac{\pi }{4}$
• D. None of these

Answer 1

The correct option is B $1004-tan1$

${\int }_0^{1004}\left[ta{n}^{-1}x\right]dx={\int }_0^{tan1}\left[ta{n}^{-1}x\right]dx+{\int }_{tan1}^{1004}\left[ta{n}^{-1}x\right]dx$
$=0+1{\int }_{tan1}^{1004}1dx=1004-tan1$