Question

$Letg\left(x\right)=minimumof\{(x+\left|x\right|),(x-\left|x\right|)\}$ then ${\int }_{-3}^{3}f\left(x\right)dx$ equals

• A. $2$
• B. $3$
• C. $1$
• D. None of these

Answer 1

The correct option is D None of these

The graph of $f\left(x\right)=min\{(x+\left|x\right|),(x-\left|x\right|)\}$ is
$\therefore {\int }_{-3}^{3}f\left(x\right)dx=6{\int }_0^{1}f\left(x\right)dx=6\times \frac{1}{2}\times 1\times \frac{1}{2}=\frac{3}{2}$