Question

The value of ${\int }_{-2}^{2}min.\left\{\left|x\right|,\left[x\right]\right\}dx$, where $[\cdot ]$ denotes the greatest integer function, is

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$

Answer 1

The correct option is B $-1$

${\int }_{-2}^{2}min\left\{\left|x\right|,\left[x\right]\right\}.dx$
In $\left(-2,2\right)\left[x\right]$ is always min than $\left|x\right|$
$\begin{array}{c}{\int }_{-2}^2\left[x\right]dx\\ {\int }_{-2}^{-1}-2.dx+{\int }_{-1}^0-1dx+{\int }_0^{1}0.dx+{\int }_1^2.1.dx\\ -2-1+0+2\\ -1\end{array}$