Question

Area of the region bounded by $y=|x-1|$ and $y=1$ is

• A. $2$ sq. units
• B. $1$ sq. units
• C. $\frac{1}{2}$ sq. units
• D. none of these

Answer 1

Answer: (B)

We have, $y = x - 1$, if $x - 1 \ge 0$
$y = - x + 1$ , if $x - 1< 0$

Required area = area of shaded region
$A=\int\limits_{0}^{2}1 dx-\left[\int\limits_{0}^{1}\left(1-x\right)dx+\int\limits_{1}^{2}\left(x-1\right)dx\right]$

$=\left[x\right]_{0}^{2}-\left[x-\frac{x^{2}}{2}\right]_{0}^{1}-\left[\frac{x^{2}}{2}-x\right]_{1}^{2}$

$=2-\frac{1}{2}-\frac{1}{2}=1$ sq. unit