Question

The area of the region bounded by the curves $y=|x-1|$ and $y=3-|x|$ is?

• A. $2$ sq. units
• B. $3$ sq. units
• C. $4$ sq. units
• D. $6$ sq. units

Answer 1

The correct option is C $4$ sq. units

$y=3(-x)$ $\Rightarrow$ $y=3+x$

$y=|x-1|\Rightarrow y=|-1|[ifx=0]$

$y=3-\left|x\right|$

$x=2$ $2y=4$

$2y=2$ $y=2$

$\Rightarrow$ $y=1$

Breadth =distance between $(1,0)$ and $(2,1)$ or $(0,3)$ and $(-1,2)$

$=\sqrt{{(2-1)}^2+{(1-0)}^2}=\sqrt{2}$

or distance between $(1,0)$ and $(2,3)$

length =Distance between $(0,3)$ and $(2,1)$ or $(-1,2)$ and $(1,0)$

$=\sqrt{{(0-2)}^2+{(3-1)}^2}=\sqrt{8}=2\sqrt{2}$

Area=length $\times$ breadth$=\sqrt{2}\times 2\sqrt{2}=4$ (units sq)