Question

If $x\ge 0$ and $y\ge 0$ then the area bounded by the graph of $\left[x\right]+\left[y\right]=2$ is (where $[.]$ denotes greatest integer fuction)

• A. $6$ sq. unit
• B. $1$ sq. unit
• C. $2$ sq. unit
• D. $3$ sq. unit

Answer 1

The correct option is A $6$ sq. unit

From $x\in (0,1),\left[x\right]=0\Rightarrow \left[y\right]=2$

In $x\in [1,2],\left[x\right]=1\Rightarrow \left[y\right]=1$

In $x\in [2,3],\left[x\right]=2\Rightarrow \left[y\right]=0$

Further $y$ would be $<0$ which is not possible

$\Rightarrow$ Area $=3+2+1=6$