Question

Area bounded by the curve $\left[|x|\right]+\left[|y|\right]=3$, where $[\cdot ]$ denotes the greatest integer function.

• A. $8$ sq. units
• B. $12$ sq. units
• C. $16$ sq. units
• D. $20$ sq. units

Answer 1

The correct option is C $16$ sq. units

$\left[|x|\right]+[\mid y\mid ].3,$ (given)

$\left[x\right]+\left[y\right]=3,x\ge 0,y\ge 0$

let $0\le x<1$

$x=0$, then $3\le y\le 4$.

let $1\le x\le 2$

$,then$

$2\le y\le 3$

let $2\le x\le 3$

$x=2$, then $1\le y\le 2$

let $3\le x\le 4$

$x=3$, then $0\le y\le 1$

Total area = 4 squnits. then $=4\times 4$

$=16$ squnits.

Answer (C) is correct.