Question

The value B $={\int }_1^{100}\left[se{c}^{-1}x\right]$ dx (where [.] denotes greatest integer funciton) is equal to

• A. $sec1$
• B. $100-sec1$
• C. $99-sec1$
• D. $sec1-100$

Answer 1

The correct option is B $100-sec1$

We have $\left[se{c}^{-1}x\right]=0$ , $1\le x\le sec\left(1\right)$
$\left[se{c}^{-1}x\right]=1$ , $sec\left(1\right)\le x\le 100$
Hence,
$I={\int }_1^{sec1}0dx+{\int }_{sec1}^{100}1dx$
$I=100-sec1$
Hence, option B is correct.