Question

The area of the region bounded by the curves $y=|x-1|andy=3-\left|x\right|$ is

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is C 4

$y=3-\left|x\right|,y=|x-1|$
If $x\ge 1$ then $3-x=x-1\Rightarrow x=2.$
If $0\le x<1.3-x=1-x$, which is not possible.
If $x<0,3+x=1-x\Rightarrow x=-1$ $\therefore x=-1,2$
Area = ${\int }_{-1}^2[3+x-(1-x\left)\right]dx+{\int }_0^1\left[\right(3-x)-(1-x\left)\right]dx+{\int }_1^2\left[\right(3-x)-(x-1\left)\right]dx$
$=1+2+1=4$ sq. unit