Question

The function $f\left(x\right)$ is defined as $|\left[x\right]x|$ for $-1<x\le 2$.
The area under the curve $y=f\left(x\right)$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$


$A_1=\frac{1}{2}\times 1\times 1=\frac{1}{2}$
$A_2=\frac{1}{2}\times 1\times 1=\frac{1}{2}$
$A_3=1\times 1=1$

$\therefore \text{Required area}=\frac{1}{2}+\frac{1}{2}+1=2\text{sq. units}$